]> AND Private Git Repository - these_gilles.git/blob - DOCS/L'estimation du gradient d'une fonction de densité, avec des applications dans Motif Recognition_ Baidu bibliothèque_files/_wk_2b04e7729dfe2503f00bb56e8dfe3e05_0(1).json
Logo AND Algorithmique Numérique Distribuée

Private GIT Repository
modif finale lnivs + keywords
[these_gilles.git] / DOCS / L'estimation du gradient d'une fonction de densité, avec des applications dans Motif Recognition_ Baidu bibliothèque_files / _wk_2b04e7729dfe2503f00bb56e8dfe3e05_0(1).json
1 wenku_2({"font":{"11b6a7de6f1aff00bed51eac0010002":"Helvetica"},"style":[{"t":"style","c":[17,27,0],"s":{"font-size":"8.64"}},{"t":"style","c":[0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,1],"s":{"font-family":"Arial"}},{"t":"style","c":[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,2],"s":{"color":"#000000"}},{"t":"style","c":[31,3],"s":{"font-size":"13.32"}},{"t":"style","c":[5,8,10,11,15,16,19,20,21,22,23,24,26,28,34,35,4],"s":{"font-size":"16.2"}},{"t":"style","c":[5],"s":{"letter-spacing":"2.545"}},{"t":"style","c":[7,12,13,14,25,32,6],"s":{"font-size":"14.76"}},{"t":"style","c":[7],"s":{"letter-spacing":"0.756"}},{"t":"style","c":[8],"s":{"letter-spacing":"1.162"}},{"t":"style","c":[9],"s":{"letter-spacing":"0.904"}},{"t":"style","c":[10],"s":{"letter-spacing":"1.059"}},{"t":"style","c":[11],"s":{"letter-spacing":"1.03"}},{"t":"style","c":[12],"s":{"letter-spacing":"0.873"}},{"t":"style","c":[13],"s":{"letter-spacing":"0.715"}},{"t":"style","c":[14],"s":{"letter-spacing":"0.825"}},{"t":"style","c":[15],"s":{"letter-spacing":"1.186"}},{"t":"style","c":[16],"s":{"letter-spacing":"1.047"}},{"t":"style","c":[17],"s":{"letter-spacing":"0.543"}},{"t":"style","c":[18],"s":{"font-size":"17.64"}},{"t":"style","c":[19],"s":{"letter-spacing":"1.046"}},{"t":"style","c":[20],"s":{"letter-spacing":"0.886"}},{"t":"style","c":[21],"s":{"letter-spacing":"1.128"}},{"t":"style","c":[22],"s":{"letter-spacing":"2.149"}},{"t":"style","c":[23],"s":{"letter-spacing":"1.229"}},{"t":"style","c":[24],"s":{"letter-spacing":"0.923"}},{"t":"style","c":[25],"s":{"letter-spacing":"0.87"}},{"t":"style","c":[26],"s":{"letter-spacing":"0.979"}},{"t":"style","c":[27],"s":{"letter-spacing":"-0.168"}},{"t":"style","c":[28],"s":{"letter-spacing":"0.975"}},{"t":"style","c":[29],"s":{"letter-spacing":"1.277"}},{"t":"style","c":[30],"s":{"letter-spacing":"1.09"}},{"t":"style","c":[31],"s":{"letter-spacing":"0.962"}},{"t":"style","c":[32],"s":{"letter-spacing":"0.522"}},{"t":"style","c":[33],"s":{"letter-spacing":"0.692"}},{"t":"style","c":[34],"s":{"letter-spacing":"1.093"}},{"t":"style","c":[35],"s":{"letter-spacing":"1.324"}}],"body":[{"c":{"ix":0,"iy":0,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":-0.299,"y0":36.42,"y1":-0.299,"y2":-0.299,"y3":36.42,"z":0},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_0.png"},"t":"pic"},{"c":{"ix":0,"iy":67,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":36.419,"y0":73.139,"y1":36.419,"y2":36.419,"y3":73.139,"z":1},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_1.png"},"t":"pic"},{"c":{"ix":0,"iy":134,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":73.14,"y0":109.86,"y1":73.14,"y2":73.14,"y3":109.86,"z":2},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_2.png"},"t":"pic"},{"c":{"ix":0,"iy":201,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":109.859,"y0":146.579,"y1":109.859,"y2":109.859,"y3":146.579,"z":3},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_3.png"},"t":"pic"},{"c":{"ix":0,"iy":268,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":146.58,"y0":183.3,"y1":146.58,"y2":146.58,"y3":183.3,"z":4},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_4.png"},"t":"pic"},{"c":{"ix":0,"iy":335,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":183.3,"y0":220.02,"y1":183.3,"y2":183.3,"y3":220.02,"z":5},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_5.png"},"t":"pic"},{"c":{"ix":0,"iy":402,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":220.02,"y0":256.74,"y1":220.02,"y2":220.02,"y3":256.74,"z":6},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_6.png"},"t":"pic"},{"c":{"ix":0,"iy":469,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":256.74,"y0":293.46,"y1":256.74,"y2":256.74,"y3":293.46,"z":7},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_7.png"},"t":"pic"},{"c":{"ix":0,"iy":536,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":293.46,"y0":330.18,"y1":293.46,"y2":293.46,"y3":330.18,"z":8},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_8.png"},"t":"pic"},{"c":{"ix":0,"iy":603,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":330.18,"y0":366.9,"y1":330.18,"y2":330.18,"y3":366.9,"z":9},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_9.png"},"t":"pic"},{"c":{"ix":0,"iy":670,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":366.9,"y0":403.62,"y1":366.9,"y2":366.9,"y3":403.62,"z":10},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_10.png"},"t":"pic"},{"c":{"ix":0,"iy":737,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":403.62,"y0":440.34,"y1":403.62,"y2":403.62,"y3":440.34,"z":11},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_11.png"},"t":"pic"},{"c":{"ix":0,"iy":804,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":440.34,"y0":477.06,"y1":440.34,"y2":440.34,"y3":477.06,"z":12},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_12.png"},"t":"pic"},{"c":{"ix":0,"iy":871,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":477.06,"y0":513.78,"y1":477.06,"y2":477.06,"y3":513.78,"z":13},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_13.png"},"t":"pic"},{"c":{"ix":0,"iy":938,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":513.78,"y0":550.5,"y1":513.78,"y2":513.78,"y3":550.5,"z":14},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_14.png"},"t":"pic"},{"c":{"ix":0,"iy":1005,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":550.5,"y0":587.22,"y1":550.5,"y2":550.5,"y3":587.22,"z":15},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_15.png"},"t":"pic"},{"c":{"ix":0,"iy":1072,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":587.219,"y0":623.939,"y1":587.219,"y2":587.219,"y3":623.939,"z":16},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_16.png"},"t":"pic"},{"c":{"ix":0,"iy":1139,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":623.939,"y0":660.66,"y1":623.939,"y2":623.939,"y3":660.66,"z":17},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_17.png"},"t":"pic"},{"c":{"ix":0,"iy":1206,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":660.66,"y0":697.38,"y1":660.66,"y2":660.66,"y3":697.38,"z":18},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_18.png"},"t":"pic"},{"c":{"ix":0,"iy":1273,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":697.379,"y0":734.099,"y1":697.379,"y2":697.379,"y3":734.099,"z":19},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_19.png"},"t":"pic"},{"c":{"ix":0,"iy":1340,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":734.099,"y0":770.819,"y1":734.099,"y2":734.099,"y3":770.819,"z":20},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_20.png"},"t":"pic"},{"c":{"ix":0,"iy":1407,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":770.819,"y0":807.54,"y1":770.819,"y2":770.819,"y3":807.54,"z":21},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_21.png"},"t":"pic"},{"c":{"ix":0,"iy":1474,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":807.54,"y0":844.26,"y1":807.54,"y2":807.54,"y3":844.26,"z":22},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_22.png"},"t":"pic"},{"c":{"ix":0,"iy":1541,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":844.26,"y0":880.98,"y1":844.26,"y2":844.26,"y3":880.98,"z":23},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_23.png"},"t":"pic"},{"c":{"ix":0,"iy":1608,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":880.98,"y0":917.7,"y1":880.98,"y2":880.98,"y3":917.7,"z":24},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_24.png"},"t":"pic"},{"c":{"ix":0,"iy":1675,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":917.7,"y0":954.42,"y1":917.7,"y2":917.7,"y3":954.42,"z":25},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_25.png"},"t":"pic"},{"c":{"ix":0,"iy":1742,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":954.42,"y0":991.14,"y1":954.42,"y2":954.42,"y3":991.14,"z":26},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_26.png"},"t":"pic"},{"c":{"ix":0,"iy":1809,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":991.139,"y0":1027.859,"y1":991.139,"y2":991.139,"y3":1027.859,"z":27},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_27.png"},"t":"pic"},{"c":{"ix":0,"iy":1876,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":1027.859,"y0":1064.58,"y1":1027.859,"y2":1027.859,"y3":1064.58,"z":28},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_28.png"},"t":"pic"},{"c":{"ix":0,"iy":1943,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":1064.58,"y0":1101.3,"y1":1064.58,"y2":1064.58,"y3":1101.3,"z":29},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_29.png"},"t":"pic"},{"c":{"ix":0,"iy":2010,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":1101.3,"y0":1138.02,"y1":1101.3,"y2":1101.3,"y3":1138.02,"z":30},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_30.png"},"t":"pic"},{"c":{"ix":0,"iy":2077,"iw":1557,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":1138.02,"y0":1174.74,"y1":1138.02,"y2":1138.02,"y3":1174.74,"z":31},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_31.png"},"t":"pic"},{"c":{"ix":0,"iy":2144,"iw":1557,"ih":22},"p":{"h":22,"opacity":1,"rotate":0,"w":915.839,"x":0,"x0":0,"x1":0,"x2":915.839,"x3":915.839,"y":1174.74,"y0":1187.7,"y1":1174.74,"y2":1174.74,"y3":1187.7,"z":32},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_2_32.png"},"t":"pic"},{"c":"FUKUNAGA ","p":{"h":9.21,"w":42.308,"x":40.68,"y":52.758,"z":33},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.779"},"t":"word","r":[0]},{"c":"AND ","p":{"h":9.21,"w":16.835,"x":101.156,"y":52.758,"z":34},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.795"},"t":"word","r":[0]},{"c":"HOSTETLER: ","p":{"h":9.21,"w":47.721,"x":127.074,"y":52.758,"z":35},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.7"},"t":"word","r":[0]},{"c":"GRADIENT ","p":{"h":9.21,"w":39.559,"x":191.151,"y":52.758,"z":36},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.725"},"t":"word","r":[0]},{"c":"OF DENSITY ","p":{"h":9.21,"w":49.517,"x":246.227,"y":52.758,"z":37},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"1.114"},"t":"word","r":[0]},{"c":"FUNCTION ","p":{"h":9.21,"w":39.508,"x":308.504,"y":52.758,"z":38},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.718"},"t":"word","r":[0]},{"c":"33 ","p":{"h":14.199,"w":15.3,"x":796.68,"y":49.098,"z":39},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.857},"s":{"letter-spacing":"1.25"},"t":"word","r":[3]},{"c":"is a function of the sample ","p":{"h":17.269,"w":179.926,"x":39.96,"y":86.224,"z":40},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.245"},"t":"word","r":[4]},{"c":"s","p":{"h":17.269,"w":6.341,"x":217.801,"y":86.224,"z":41},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ize ","p":{"h":17.269,"w":21.971,"x":225.125,"y":86.224,"z":42},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.982"},"t":"word","r":[4]},{"c":"N","p":{"h":17.269,"w":9.116,"x":245.521,"y":86.224,"z":43},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":", is chosen to satisfy ","p":{"h":17.269,"w":136.632,"x":255.415,"y":86.224,"z":44},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.985"},"t":"word","r":[4]},{"c":"functions that satisfy ","p":{"h":17.269,"w":137.526,"x":433.799,"y":86.224,"z":48},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.926"},"t":"word","r":[4]},{"c":"lim h(N) = 0 ","p":{"h":17.269,"w":95.071,"x":183.96,"y":113.944,"z":45},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[5]},{"c":"(6) ","p":{"h":15.734,"w":19.015,"x":398.879,"y":117.701,"z":46},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[7]},{"c":"lixq, p(X) = 0, ","p":{"h":17.269,"w":106.827,"x":574.92,"y":107.464,"z":49},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.05"},"t":"word","r":[4]},{"c":"(15) ","p":{"h":17.269,"w":30.213,"x":784.802,"y":110.704,"z":51},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"N-W ","p":{"h":9.21,"w":16.146,"x":180.72,"y":132.678,"z":47},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.743"},"t":"word","r":[0]},{"c":"Ilxll-~ ","p":{"h":17.269,"w":37.359,"x":565.92,"y":121.504,"z":50},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.572"},"t":"word","r":[4]},{"c":"to guarantee asymptotic unbiasedness of the estimate. ","p":{"h":17.269,"w":383.03,"x":39.957,"y":149.584,"z":52},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.439"},"t":"word","r":[4]},{"c":"Although the condition (15) ","p":{"h":17.269,"w":181.054,"x":433.439,"y":143.464,"z":60},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.049"},"t":"word","r":[4]},{"c":"m","p":{"h":17.269,"w":10.305,"x":612.001,"y":143.464,"z":61},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ust be ","p":{"h":17.269,"w":42.58,"x":623.503,"y":143.464,"z":62},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.098"},"t":"word","r":[4]},{"c":"i","p":{"h":17.269,"w":2.774,"x":664.921,"y":143.464,"z":63},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"mposed ","p":{"h":17.269,"w":55.585,"x":669.031,"y":143.464,"z":64},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.335"},"t":"word","r":[4]},{"c":"o","p":{"h":17.269,"w":7.134,"x":721.441,"y":143.464,"z":65},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"n the density ","p":{"h":17.269,"w":84.611,"x":730.132,"y":143.464,"z":66},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"font-size":"16.2"},"t":"word","r":[4,9]},{"c":"Mean-square consistency of the estimate ","p":{"h":17.269,"w":267.838,"x":40.317,"y":167.584,"z":53},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.931"},"t":"word","r":[4]},{"c":"i","p":{"h":17.269,"w":2.774,"x":306.719,"y":167.584,"z":54},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"s assured by the ","p":{"h":17.269,"w":110.071,"x":310.133,"y":167.584,"z":55},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.016"},"t":"word","r":[4]},{"c":"function, practically all ","p":{"h":17.269,"w":164.281,"x":433.439,"y":161.464,"z":67},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.507"},"t":"word","r":[4]},{"c":"density functions satisfy this ","p":{"h":17.269,"w":204.5,"x":607.681,"y":161.464,"z":68},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.521"},"t":"word","r":[4]},{"c":"condition ","p":{"h":17.269,"w":63.357,"x":39.957,"y":185.224,"z":56},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[10]},{"c":"condition. Thus ","p":{"h":17.269,"w":105.007,"x":433.439,"y":179.104,"z":69},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.143"},"t":"word","r":[4]},{"c":"lim A%\u201c(N) = co. ","p":{"h":17.269,"w":125.36,"x":169.198,"y":203.944,"z":57},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.893"},"t":"word","r":[4]},{"c":"lim ","p":{"h":15.734,"w":18.78,"x":531.719,"y":205.901,"z":70},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.63"},"t":"word","r":[6]},{"c":"E{Q,p,(X)) ","p":{"h":15.734,"w":61.903,"x":560.52,"y":205.901,"z":71},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.744"},"t":"word","r":[6]},{"c":"= V,p(X) ","p":{"h":15.734,"w":56.642,"x":646.922,"y":205.901,"z":72},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.615"},"t":"word","r":[6]},{"c":"N-tm ","p":{"h":9.21,"w":17.507,"x":165.6,"y":222.318,"z":59},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.611"},"t":"word","r":[0]},{"c":"(7) ","p":{"h":17.269,"w":21.666,"x":398.52,"y":206.464,"z":58},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[11]},{"c":"N-CO ","p":{"h":9.21,"w":20.39,"x":528.84,"y":220.878,"z":73},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.719"},"t":"word","r":[0]},{"c":"(16) ","p":{"h":15.734,"w":26.448,"x":784.439,"y":206.261,"z":74},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"Uniform ","p":{"h":17.269,"w":54.541,"x":39.96,"y":239.584,"z":75},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.066"},"t":"word","r":[4]},{"c":"consistency (in probability) is assured ","p":{"h":17.269,"w":267.773,"x":104.4,"y":239.584,"z":76},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.426"},"t":"word","r":[4]},{"c":"b","p":{"h":17.269,"w":7.134,"x":371.161,"y":239.584,"z":77},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"y the ","p":{"h":17.269,"w":40.225,"x":379.621,"y":239.584,"z":78},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.209"},"t":"word","r":[4]},{"c":"at the points of continuity of ","p":{"h":17.269,"w":202.947,"x":433.442,"y":238.144,"z":79},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.611"},"t":"word","r":[4]},{"c":"V,p(X), ","p":{"h":15.734,"w":42.941,"x":641.879,"y":239.381,"z":80},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[13]},{"c":"provided that 1) ","p":{"h":17.269,"w":114.674,"x":699.48,"y":238.144,"z":81},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.544"},"t":"word","r":[4]},{"c":"condition ","p":{"h":17.269,"w":63.357,"x":39.596,"y":257.584,"z":82},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[10]},{"c":"p(X) ","p":{"h":15.734,"w":27.368,"x":431.64,"y":257.381,"z":83},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[14]},{"c":"satisfies (15); 2) h(N) goes ","p":{"h":17.269,"w":184.457,"x":469.799,"y":256.144,"z":84},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.231"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":653.041,"y":256.144,"z":85},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"o zero as N -+ co (see ","p":{"h":17.269,"w":160.06,"x":657.531,"y":256.144,"z":86},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.692"},"t":"word","r":[4]},{"c":"lim FIJI?\u201c(N) = co, ","p":{"h":17.269,"w":131.84,"x":166.318,"y":276.304,"z":87},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.476"},"t":"word","r":[4]},{"c":"I","p":{"h":17.269,"w":3.567,"x":676.801,"y":274.144,"z":96},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ap(Y)\/ayil ","p":{"h":17.269,"w":65.376,"x":681.224,"y":274.144,"z":97},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.855"},"t":"word","r":[4]},{"c":"dY < CO, ","p":{"h":15.734,"w":68.258,"x":747.719,"y":275.381,"z":98},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.595"},"t":"word","r":[6]},{"c":"N\u2019G) ","p":{"h":9.21,"w":17.024,"x":163.079,"y":294.678,"z":99},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.049"},"t":"word","r":[0]},{"c":"(8) ","p":{"h":15.734,"w":19.015,"x":398.159,"y":280.061,"z":88},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[7]},{"c":"(6)); 3) ","p":{"h":17.269,"w":46.634,"x":433.439,"y":274.144,"z":89},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.73"},"t":"word","r":[4]},{"c":"k","p":{"h":17.269,"w":6.341,"x":478.08,"y":274.144,"z":90},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"(X) satisfies (2)--(5); and ","p":{"h":17.269,"w":154.124,"x":485.369,"y":274.144,"z":91},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.552"},"t":"word","r":[4]},{"c":"4","p":{"h":17.269,"w":7.134,"x":637.921,"y":274.144,"z":92},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":") ","p":{"h":17.269,"w":8.097,"x":646.218,"y":274.144,"z":93},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"s","p":{"h":17.269,"w":6.341,"x":653.041,"y":274.144,"z":94},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"R\u201d ","p":{"h":17.269,"w":21.921,"x":660.562,"y":274.144,"z":95},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"-0.56"},"t":"word","r":[4]},{"c":"for ","p":{"h":17.269,"w":20.572,"x":432.719,"y":291.784,"z":100},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.871"},"t":"word","r":[4]},{"c":"i = ","p":{"h":15.734,"w":20.507,"x":456.84,"y":293.021,"z":101},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.896"},"t":"word","r":[6]},{"c":"1,2; * ","p":{"h":17.269,"w":39.483,"x":485.64,"y":291.784,"z":102},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.264"},"t":"word","r":[4]},{"c":"*","p":{"h":17.269,"w":4.756,"x":523.8,"y":291.784,"z":103},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":",n. ","p":{"h":17.269,"w":19.552,"x":529.308,"y":291.784,"z":104},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.751"},"t":"word","r":[4]},{"c":"provided the true density ","p":{"h":17.269,"w":175.023,"x":39.237,"y":311.584,"z":105},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.395"},"t":"word","r":[4]},{"c":"p(X) ","p":{"h":15.734,"w":27.368,"x":214.56,"y":312.821,"z":106},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[14]},{"c":"is uniformly continuous. ","p":{"h":17.269,"w":168.516,"x":253.44,"y":311.584,"z":107},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.414"},"t":"word","r":[4]},{"c":"The proof is given ","p":{"h":17.269,"w":122.174,"x":447.481,"y":309.784,"z":112},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.167"},"t":"word","r":[4]},{"c":"i","p":{"h":17.269,"w":2.774,"x":568.081,"y":309.784,"z":113},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"n the Appendix. ","p":{"h":17.269,"w":107.516,"x":571.727,"y":309.784,"z":114},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[15]},{"c":"Additional conditions were found by Van Ryzin [6] to ","p":{"h":17.269,"w":378.628,"x":39.238,"y":329.584,"z":108},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.712"},"t":"word","r":[4]},{"c":"assure strong and uniformly ","p":{"h":17.269,"w":199.397,"x":39.238,"y":347.944,"z":109},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.57"},"t":"word","r":[4]},{"c":"strong consistency (with ","p":{"h":17.269,"w":167.539,"x":249.479,"y":347.944,"z":110},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.255"},"t":"word","r":[4]},{"c":"C. Consistency ","p":{"h":15.734,"w":96.463,"x":433.799,"y":341.261,"z":115},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.321"},"t":"word","r":[6]},{"c":"probability one). ","p":{"h":17.269,"w":112.532,"x":39.238,"y":365.584,"z":111},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.149"},"t":"word","r":[4]},{"c":"The estimate ","p":{"h":17.269,"w":88.197,"x":447.482,"y":364.144,"z":136},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.136"},"t":"word","r":[4]},{"c":"v","p":{"h":15.734,"w":5.637,"x":533.52,"y":365.381,"z":137},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[6]},{"c":"xpN(X) ","p":{"h":15.734,"w":43.338,"x":540.101,"y":365.381,"z":138},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.944"},"t":"word","r":[6]},{"c":"is consistent ","p":{"h":17.269,"w":85.228,"x":592.2,"y":364.144,"z":139},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.981"},"t":"word","r":[4]},{"c":"i","p":{"h":17.269,"w":2.774,"x":673.92,"y":364.144,"z":140},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"n quadratic ","p":{"h":17.269,"w":79.447,"x":677.566,"y":364.144,"z":141},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.28"},"t":"word","r":[4]},{"c":"m","p":{"h":17.269,"w":10.305,"x":755.64,"y":364.144,"z":142},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ean, ","p":{"h":17.269,"w":32.77,"x":767.307,"y":364.144,"z":143},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.361"},"t":"word","r":[4]},{"c":"Motivated by this general ","p":{"h":17.269,"w":172.105,"x":54,"y":383.944,"z":116},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.215"},"t":"word","r":[4]},{"c":"c","p":{"h":17.269,"w":6.341,"x":222.121,"y":383.944,"z":117},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"lass ","p":{"h":17.269,"w":29.359,"x":229.467,"y":383.944,"z":118},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.004"},"t":"word","r":[4]},{"c":"o","p":{"h":17.269,"w":7.134,"x":256.321,"y":383.944,"z":119},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"f nonparametric ","p":{"h":17.269,"w":109.234,"x":264.379,"y":383.944,"z":120},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.244"},"t":"word","r":[4]},{"c":"d","p":{"h":17.269,"w":7.134,"x":370.801,"y":383.944,"z":121},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ensity ","p":{"h":17.269,"w":42.28,"x":378.984,"y":383.944,"z":122},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[16]},{"c":"estimates, we use the differentiable kernel function and ","p":{"h":17.269,"w":380.655,"x":39.24,"y":401.944,"z":123},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.309"},"t":"word","r":[4]},{"c":"N-too ","p":{"h":9.21,"w":19.841,"x":502.56,"y":410.598,"z":148},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[17]},{"c":"lim ","p":{"h":18.804,"w":21.424,"x":505.439,"y":393.507,"z":144},"ps":{"_opacity":1,"_scaleX":0.878},"s":{"letter-spacing":"0.914"},"t":"word","r":[18]},{"c":"E{IIQ,PN(X) ","p":{"h":9.21,"w":41.436,"x":533.879,"y":401.238,"z":145},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.553"},"t":"word","r":[0]},{"c":"- V,P<X)II~) = 0 ","p":{"h":18.804,"w":121.322,"x":622.079,"y":393.507,"z":146},"ps":{"_opacity":1,"_scaleX":0.878},"s":{"letter-spacing":"1.654"},"t":"word","r":[18]},{"c":"(17) ","p":{"h":17.269,"w":30.213,"x":784.439,"y":394.384,"z":147},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"then estimate the density gradient as the gradient of the ","p":{"h":17.269,"w":380.247,"x":39.24,"y":420.304,"z":124},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.232"},"t":"word","r":[4]},{"c":"density ","p":{"h":17.269,"w":50.462,"x":39.24,"y":438.304,"z":125},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[16]},{"c":"e","p":{"h":17.269,"w":7.134,"x":87.48,"y":438.304,"z":126},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"stimate ","p":{"h":17.269,"w":50.855,"x":95.662,"y":438.304,"z":127},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"(","p":{"h":17.269,"w":4.36,"x":143.64,"y":438.304,"z":128},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"1). This gives ","p":{"h":17.269,"w":89.174,"x":148.846,"y":438.304,"z":129},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[20]},{"c":"t","p":{"h":17.269,"w":3.567,"x":235.081,"y":438.304,"z":130},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"he density ","p":{"h":17.269,"w":69.521,"x":239.782,"y":438.304,"z":131},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.951"},"t":"word","r":[4]},{"c":"g","p":{"h":17.269,"w":7.134,"x":307.441,"y":438.304,"z":132},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"radient ","p":{"h":17.269,"w":49.751,"x":315.704,"y":438.304,"z":133},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[21]},{"c":"e","p":{"h":17.269,"w":7.134,"x":363.242,"y":438.304,"z":134},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"stimate ","p":{"h":17.269,"w":50.855,"x":371.423,"y":438.304,"z":135},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"at the points of continuity of ","p":{"h":17.269,"w":198.627,"x":433.079,"y":427.864,"z":149},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.467"},"t":"word","r":[4]},{"c":"V,p(X), ","p":{"h":15.734,"w":42.941,"x":636.48,"y":429.101,"z":150},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[13]},{"c":"provided that the ","p":{"h":17.269,"w":119.245,"x":693.719,"y":427.864,"z":151},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.347"},"t":"word","r":[4]},{"c":"following conditions are. satisfied ","p":{"h":17.269,"w":215.88,"x":433.078,"y":445.864,"z":152},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.821"},"t":"word","r":[4]},{"c":"6,p,(X) ","p":{"h":17.269,"w":47.688,"x":80.276,"y":474.664,"z":153},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.912"},"t":"word","r":[4]},{"c":"E (Nh\u201d)-1 5 ","p":{"h":17.269,"w":87.871,"x":143.276,"y":474.664,"z":154},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.907"},"t":"word","r":[4]},{"c":"V,k(h-l(X ","p":{"h":17.269,"w":60.205,"x":242.277,"y":474.664,"z":155},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.861"},"t":"word","r":[4]},{"c":"- X,)) ","p":{"h":17.269,"w":43.911,"x":318.957,"y":474.664,"z":156},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[22]},{"c":"lim h(N) = 0 ","p":{"h":17.269,"w":95.071,"x":576.36,"y":472.864,"z":160},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[5]},{"c":"j=l ","p":{"h":9.21,"w":9.374,"x":216,"y":493.038,"z":157},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.398"},"t":"word","r":[0]},{"c":"(9) ","p":{"h":17.269,"w":21.666,"x":398.159,"y":476.824,"z":158},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[11]},{"c":"1) ","p":{"h":17.269,"w":16.393,"x":434.52,"y":476.464,"z":159},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"N+CX ","p":{"h":9.21,"w":21.293,"x":573.48,"y":491.238,"z":162},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.758"},"t":"word","r":[0]},{"c":"(18) ","p":{"h":17.269,"w":30.213,"x":784.082,"y":475.744,"z":161},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"= (Nh\u201d+l)-\u2019 j$l Vk(h-\u2018(X ","p":{"h":17.269,"w":171.905,"x":142.92,"y":520.024,"z":167},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[23]},{"c":"- X,)) ","p":{"h":17.269,"w":43.911,"x":329.041,"y":520.024,"z":168},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[22]},{"c":"(10) ","p":{"h":17.269,"w":30.213,"x":390.961,"y":519.304,"z":169},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"lim N\/I\u201d+\u2018(N) ","p":{"h":17.269,"w":87.493,"x":556.2,"y":508.864,"z":163},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.793"},"t":"word","r":[4]},{"c":"= co ","p":{"h":17.269,"w":36.521,"x":656.64,"y":508.864,"z":164},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.673"},"t":"word","r":[4]},{"c":"N-+CC ","p":{"h":9.21,"w":24.381,"x":553.319,"y":527.958,"z":166},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.694"},"t":"word","r":[0]},{"c":"(19) ","p":{"h":17.269,"w":30.213,"x":784.081,"y":511.744,"z":165},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"and in addition to (2)-(5) the kernel ","p":{"h":17.269,"w":232.5,"x":432.722,"y":544.864,"z":250},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.036"},"t":"word","r":[4]},{"c":"f","p":{"h":17.269,"w":3.567,"x":664.203,"y":544.864,"z":251},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"unction is such ","p":{"h":17.269,"w":101.709,"x":668.781,"y":544.864,"z":252},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.075"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":768.244,"y":544.864,"z":253},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"hat ","p":{"h":17.269,"w":23.444,"x":772.734,"y":544.864,"z":254},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[24]},{"c":"Vk(Y) = ","p":{"h":17.269,"w":59.134,"x":101.519,"y":574.024,"z":170},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.1"},"t":"word","r":[4]},{"c":"ak(Y) ","p":{"h":15.734,"w":34.006,"x":174.96,"y":566.261,"z":171},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"ak(Y) ","p":{"h":15.734,"w":34.006,"x":224.281,"y":566.261,"z":172},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"(11) ","p":{"h":15.734,"w":26.448,"x":390.604,"y":577.061,"z":175},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"2) ","p":{"h":15.734,"w":14.485,"x":433.079,"y":576.701,"z":255},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"sup ","p":{"h":17.269,"w":27.127,"x":564.48,"y":572.224,"z":256},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.401"},"t":"word","r":[4]},{"c":"Iki\u2019(Y)I ","p":{"h":15.734,"w":39.441,"x":595.079,"y":573.461,"z":257},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.04"},"t":"word","r":[6]},{"c":"< 00 ","p":{"h":15.734,"w":35.616,"x":647.281,"y":573.461,"z":258},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.943"},"t":"word","r":[6]},{"c":"ay,\u2018-\u2018\u201c\u201d ","p":{"h":15.734,"w":43.785,"x":173.879,"y":590.381,"z":173},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-1.07"},"t":"word","r":[6]},{"c":"8Y2 ","p":{"h":15.734,"w":25.758,"x":232.201,"y":590.021,"z":174},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.159"},"t":"word","r":[6]},{"c":"YER\u201d ","p":{"h":9.21,"w":21.292,"x":561.599,"y":590.958,"z":259},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.295"},"t":"word","r":[0]},{"c":"WY ","p":{"h":15.734,"w":22.759,"x":783.72,"y":576.341,"z":260},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.475"},"t":"word","r":[6]},{"c":"and V, is the usual gradient operator with respect ","p":{"h":17.269,"w":340.539,"x":38.16,"y":612.544,"z":176},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.332"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":376.562,"y":612.544,"z":177},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"o x1, ","p":{"h":17.269,"w":37.709,"x":381.052,"y":612.544,"z":178},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.583"},"t":"word","r":[4]},{"c":"x2, ","p":{"h":17.269,"w":22.759,"x":38.16,"y":630.904,"z":179},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[26]},{"c":"*","p":{"h":17.269,"w":4.756,"x":59.4,"y":630.904,"z":180},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":" ","p":{"h":17.269,"w":2.895,"x":65.028,"y":630.904,"z":181},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"*","p":{"h":17.269,"w":4.756,"x":66.6,"y":630.904,"z":182},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":" ","p":{"h":17.269,"w":2.895,"x":72.228,"y":630.904,"z":183},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"*","p":{"h":17.269,"w":4.756,"x":73.8,"y":630.904,"z":184},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":",","p":{"h":17.269,"w":3.567,"x":78.84,"y":630.904,"z":186},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":" ","p":{"h":17.269,"w":2.895,"x":79.428,"y":630.904,"z":185},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"x,. ","p":{"h":17.269,"w":18.264,"x":82.898,"y":630.904,"z":187},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.49"},"t":"word","r":[4]},{"c":"s ","p":{"h":14.199,"w":7.924,"x":554.04,"y":633.378,"z":261},"ps":{"_opacity":1,"_scaleX":0.857},"s":{"letter-spacing":"1.01"},"t":"word","r":[3]},{"c":"Iki\u2019(Y)l ","p":{"h":15.734,"w":38.613,"x":579.599,"y":618.821,"z":262},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.019"},"t":"word","r":[6]},{"c":"dY ~ 00 ","p":{"h":15.734,"w":61.896,"x":629.641,"y":618.821,"z":263},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"3.154"},"t":"word","r":[6]},{"c":"(21) ","p":{"h":15.734,"w":26.448,"x":783.364,"y":621.341,"z":264},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R\u201d ","p":{"h":9.21,"w":11.447,"x":561.96,"y":639.198,"z":265},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[27]},{"c":"Equation (10) ","p":{"h":17.269,"w":93.573,"x":52.92,"y":648.904,"z":188},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"i","p":{"h":17.269,"w":2.774,"x":144.721,"y":648.904,"z":189},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"s the general form of our density gradient ","p":{"h":17.269,"w":272.761,"x":148.135,"y":648.904,"z":190},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.019"},"t":"word","r":[4]},{"c":"estimates. ","p":{"h":17.269,"w":70.409,"x":38.16,"y":666.904,"z":191},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[28]},{"c":"A","p":{"h":17.269,"w":8.323,"x":104.76,"y":666.904,"z":192},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"s in density estimation, this is a kernel class ","p":{"h":17.269,"w":289.696,"x":114.211,"y":666.904,"z":193},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1"},"t":"word","r":[4]},{"c":"o","p":{"h":17.269,"w":7.134,"x":401.762,"y":666.904,"z":194},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"f ","p":{"h":17.269,"w":7.328,"x":409.82,"y":666.904,"z":195},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[24]},{"c":"lim ","p":{"h":17.269,"w":19.894,"x":555.48,"y":657.184,"z":267},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.739"},"t":"word","r":[4]},{"c":"I[ ","p":{"h":17.269,"w":11.251,"x":592.921,"y":656.824,"z":268},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.289"},"t":"word","r":[4]},{"c":"Y","p":{"h":17.269,"w":8.323,"x":600.121,"y":656.824,"z":269},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":" \/\u201ck,\u2018(Y) = 0 ","p":{"h":17.269,"w":87.026,"x":609.606,"y":656.824,"z":270},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.29"},"t":"word","r":[4]},{"c":"(22) ","p":{"h":15.734,"w":26.448,"x":783.36,"y":660.221,"z":271},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"estimates, ","p":{"h":17.269,"w":70.409,"x":37.8,"y":684.904,"z":196},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[28]},{"c":"a","p":{"h":17.269,"w":7.134,"x":105.12,"y":684.904,"z":197},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"nd various kernel functions k(Y) may be used. ","p":{"h":17.269,"w":308.037,"x":113.811,"y":684.904,"z":198},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.199"},"t":"word","r":[4]},{"c":"where ","p":{"h":17.269,"w":43.96,"x":432,"y":684.544,"z":266},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.34"},"t":"word","r":[4]},{"c":"IIYII-rm ","p":{"h":14.199,"w":39.797,"x":547.92,"y":673.698,"z":272},"ps":{"_opacity":1,"_scaleX":0.857},"s":{"letter-spacing":"0.624"},"t":"word","r":[3]},{"c":"Conditions on the kernel functions and h(N) will now be ","p":{"h":17.269,"w":380.604,"x":38.52,"y":703.264,"z":199},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.372"},"t":"word","r":[4]},{"c":"derived ","p":{"h":17.269,"w":52.841,"x":38.16,"y":721.264,"z":200},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.181"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":89.28,"y":721.264,"z":201},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"o guarantee asymptotic unbiasedness, ","p":{"h":17.269,"w":255.403,"x":93.771,"y":721.264,"z":202},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.025"},"t":"word","r":[4]},{"c":"consistency, ","p":{"h":17.269,"w":85.326,"x":339.122,"y":721.264,"z":203},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.038"},"t":"word","r":[4]},{"c":"k,\u2018(Y) ","p":{"h":15.734,"w":33.2,"x":567,"y":711.701,"z":273},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-0.029"},"t":"word","r":[6]},{"c":"E y. ","p":{"h":15.734,"w":29.481,"x":611.64,"y":711.701,"z":274},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.052"},"t":"word","r":[6]},{"c":"(23) ","p":{"h":17.269,"w":30.213,"x":783.36,"y":713.344,"z":276},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"and uniform consistency of the estimate. ","p":{"h":17.269,"w":265.309,"x":37.8,"y":739.264,"z":204},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[26]},{"c":"1 ","p":{"h":15.734,"w":9.69,"x":654.121,"y":727.541,"z":275},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.223"},"t":"word","r":[6]},{"c":"The ","p":{"h":14.199,"w":22.335,"x":431.64,"y":750.378,"z":277},"ps":{"_opacity":1,"_scaleX":0.857},"s":{"letter-spacing":"1.21"},"t":"word","r":[3]},{"c":"proof is given ","p":{"h":17.269,"w":93.014,"x":460.799,"y":747.904,"z":278},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.125"},"t":"word","r":[4]},{"c":"i","p":{"h":17.269,"w":2.774,"x":552.6,"y":747.904,"z":279},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"n the Appendix. ","p":{"h":17.269,"w":107.156,"x":556.246,"y":747.904,"z":280},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"B. Asymptotic ","p":{"h":15.734,"w":87.367,"x":37.8,"y":773.621,"z":205},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[6,29]},{"c":"Unbiasedness ","p":{"h":15.734,"w":87.239,"x":135.002,"y":773.621,"z":206},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[6,30]},{"c":"The additional power of two in the condition (19) on ","p":{"h":17.269,"w":364.764,"x":446.04,"y":765.544,"z":281},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.558"},"t":"word","r":[4]},{"c":"The basic result needed ","p":{"h":17.269,"w":172.007,"x":52.199,"y":796.144,"z":207},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.591"},"t":"word","r":[4]},{"c":"f","p":{"h":17.269,"w":3.567,"x":222.84,"y":796.144,"z":208},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"or the proof of asymptotic ","p":{"h":17.269,"w":191.498,"x":227.279,"y":796.144,"z":209},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.84"},"t":"word","r":[4]},{"c":"h(N) comes from estimating gradients and not just ","p":{"h":17.269,"w":350.301,"x":431.28,"y":783.544,"z":282},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.477"},"t":"word","r":[4]},{"c":"the ","p":{"h":14.199,"w":18.796,"x":788.039,"y":786.018,"z":283},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.857},"t":"word","r":[31]},{"c":"unbiasedness ","p":{"h":17.269,"w":97.188,"x":37.439,"y":814.144,"z":210},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.326"},"t":"word","r":[4]},{"c":"is [4, theorem 2.11. ","p":{"h":17.269,"w":130.446,"x":123.84,"y":814.144,"z":211},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.02"},"t":"word","r":[4]},{"c":"T","p":{"h":17.269,"w":7.531,"x":252.72,"y":814.144,"z":212},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"his theorem, given here ","p":{"h":17.269,"w":159.184,"x":261.375,"y":814.144,"z":213},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.14"},"t":"word","r":[4]},{"c":"density ","p":{"h":17.269,"w":50.462,"x":431.64,"y":801.544,"z":284},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[16]},{"c":"s","p":{"h":17.269,"w":6.341,"x":480.96,"y":801.544,"z":285},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"o that ","p":{"h":17.269,"w":38.628,"x":488.626,"y":801.544,"z":286},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.809"},"t":"word","r":[4]},{"c":"in (17), ","p":{"h":14.199,"w":44.285,"x":529.2,"y":804.018,"z":287},"ps":{"_opacity":1,"_scaleX":0.857},"s":{"letter-spacing":"1.423"},"t":"word","r":[3]},{"c":"without proof, states that if the function k(X) satisfies ","p":{"h":17.269,"w":384.963,"x":37.439,"y":832.144,"z":214},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.612"},"t":"word","r":[4]},{"c":"conditions (2)-(4), h(N) satisfies condition (6), and g(X) ","p":{"h":17.269,"w":377.078,"x":37.439,"y":850.144,"z":215},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[23]},{"c":"2, ","p":{"h":15.734,"w":13.699,"x":452.879,"y":839.501,"z":288},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.78"},"t":"word","r":[6]},{"c":"k(h-l(X ","p":{"h":15.734,"w":41.207,"x":477.36,"y":839.501,"z":289},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.72"},"t":"word","r":[6]},{"c":"- ","p":{"h":15.734,"w":7.315,"x":538.201,"y":839.501,"z":290},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[32]},{"c":"Y)) ","p":{"h":15.734,"w":19.953,"x":556.922,"y":839.141,"z":292},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[6,33]},{"c":"\u2019 ","p":{"h":15.734,"w":10.68,"x":586.802,"y":839.141,"z":291},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-3.644"},"t":"word","r":[6]},{"c":"= h-2[ki\u2019(h-\u2018(X ","p":{"h":15.734,"w":87.92,"x":599.76,"y":838.781,"z":294},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.644"},"t":"word","r":[6]},{"c":"- ","p":{"h":15.734,"w":7.315,"x":716.042,"y":838.781,"z":295},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[32]},{"c":"Y))12 ","p":{"h":15.734,"w":34.844,"x":734.403,"y":838.781,"z":296},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[6,9]},{"c":"(24) ","p":{"h":15.734,"w":26.448,"x":783.004,"y":838.781,"z":297},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"is any other function such ","p":{"h":17.269,"w":172.888,"x":37.439,"y":868.144,"z":216},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.111"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":208.44,"y":868.144,"z":217},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"hat ","p":{"h":17.269,"w":23.444,"x":212.931,"y":868.144,"z":218},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[24]},{"c":". b ","p":{"h":15.734,"w":17.97,"x":460.796,"y":854.621,"z":298},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.068"},"t":"word","r":[6]},{"c":"1 ","p":{"h":49.505,"w":30.976,"x":578.52,"y":824.528,"z":293},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"s":{"font-size":"46.44","letter-spacing":"3.989"},"t":"word","r":[1]},{"c":"with the additional ","p":{"h":17.269,"w":129.54,"x":430.919,"y":877.144,"z":299},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.375"},"t":"word","r":[4]},{"c":"h-\u2019 ","p":{"h":15.734,"w":22.644,"x":564.12,"y":878.381,"z":300},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-0.632"},"t":"word","r":[6]},{"c":"being generated. This additional ","p":{"h":17.269,"w":215.581,"x":595.079,"y":877.144,"z":301},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.064"},"t":"word","r":[4]},{"c":"s ","p":{"h":17.269,"w":10.086,"x":160.2,"y":917.464,"z":219},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[34]},{"c":"Is( ","p":{"h":18.804,"w":20.792,"x":185.76,"y":906.147,"z":220},"ps":{"_opacity":1,"_scaleX":0.878},"s":{"letter-spacing":"0.816"},"t":"word","r":[18]},{"c":"dY < *, ","p":{"h":18.804,"w":58.24,"x":230.397,"y":906.147,"z":221},"ps":{"_opacity":1,"_scaleX":0.878},"s":{"letter-spacing":"2.351"},"t":"word","r":[18]},{"c":"(12) ","p":{"h":15.734,"w":26.448,"x":389.52,"y":908.261,"z":222},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"power requires ","p":{"h":17.269,"w":103.386,"x":430.918,"y":895.144,"z":302},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.224"},"t":"word","r":[4]},{"c":"h","p":{"h":15.734,"w":6.341,"x":532.439,"y":896.381,"z":303},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[6]},{"c":"(N) ","p":{"h":15.734,"w":20.986,"x":539.65,"y":896.381,"z":304},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.868"},"t":"word","r":[6]},{"c":"to go to zero slightly slower than in ","p":{"h":17.269,"w":240.628,"x":568.8,"y":895.144,"z":305},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.297"},"t":"word","r":[4]},{"c":"R\u201d ","p":{"h":9.21,"w":11.447,"x":167.76,"y":926.118,"z":223},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[27]},{"c":"the ","p":{"h":14.199,"w":18.796,"x":430.919,"y":915.618,"z":306},"ps":{"_opacity":1,"_scaleX":0.857},"t":"word","r":[31]},{"c":"previous ","p":{"h":17.269,"w":60.288,"x":455.4,"y":913.144,"z":307},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.17"},"t":"word","r":[4]},{"c":"c","p":{"h":17.269,"w":6.341,"x":513.72,"y":913.144,"z":308},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"ase ","p":{"h":17.269,"w":26.98,"x":521.386,"y":913.144,"z":309},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[35]},{"c":"(","p":{"h":17.269,"w":4.36,"x":544.68,"y":913.144,"z":310},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"7) for density ","p":{"h":17.269,"w":89.712,"x":550.071,"y":913.144,"z":311},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.029"},"t":"word","r":[4]},{"c":"e","p":{"h":17.269,"w":7.134,"x":638.641,"y":913.144,"z":312},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"stimation alone. ","p":{"h":17.269,"w":106.621,"x":646.787,"y":913.144,"z":313},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.977"},"t":"word","r":[4]},{"c":"then the sequence of functions gN(X) defined ","p":{"h":17.269,"w":292.59,"x":37.44,"y":943.384,"z":224},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[20]},{"c":"b","p":{"h":17.269,"w":7.134,"x":327.241,"y":943.384,"z":225},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"y ","p":{"h":17.269,"w":10.062,"x":335.701,"y":943.384,"z":226},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[35]},{"c":"Since we may want to use the estimate of the density ","p":{"h":17.269,"w":366.904,"x":446.039,"y":930.784,"z":314},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.419"},"t":"word","r":[4]},{"c":"gradient over the ent.ire ","p":{"h":17.269,"w":160.317,"x":431.279,"y":948.784,"z":315},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.995"},"t":"word","r":[4]},{"c":"s","p":{"h":17.269,"w":6.341,"x":588.24,"y":948.784,"z":316},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"pace in the same ","p":{"h":17.269,"w":113.884,"x":595.953,"y":948.784,"z":317},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"font-size":"16.2"},"t":"word","r":[4,30]},{"c":"a","p":{"h":17.269,"w":7.134,"x":707.401,"y":948.784,"z":318},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"pplication and ","p":{"h":17.269,"w":96.373,"x":715.561,"y":948.784,"z":319},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.156"},"t":"word","r":[4]},{"c":"gN(X) = h-\u201c(N) ","p":{"h":17.269,"w":106.594,"x":64.08,"y":980.104,"z":227},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.501"},"t":"word","r":[4]},{"c":"s ","p":{"h":17.269,"w":10.086,"x":178.56,"y":993.064,"z":228},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[34]},{"c":"k(h-\u2018(N)Y)g(X ","p":{"h":15.734,"w":80.007,"x":203.76,"y":981.341,"z":229},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.481"},"t":"word","r":[6]},{"c":"- ","p":{"h":15.734,"w":7.315,"x":315.722,"y":981.341,"z":230},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[32]},{"c":"Y) dY ","p":{"h":15.734,"w":39.469,"x":334.442,"y":981.341,"z":231},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.918"},"t":"word","r":[6]},{"c":"(13) ","p":{"h":17.269,"w":30.213,"x":389.52,"y":980.104,"z":232},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"not just be satisfied with pointwise properties, we would ","p":{"h":17.269,"w":378.883,"x":431.28,"y":966.784,"z":320},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.235"},"t":"word","r":[4]},{"c":"like to determine ","p":{"h":17.269,"w":117.958,"x":430.919,"y":984.784,"z":321},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.362"},"t":"word","r":[4]},{"c":"t","p":{"h":17.269,"w":3.567,"x":547.2,"y":984.784,"z":322},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"he conditions under which ","p":{"h":17.269,"w":175.387,"x":551.902,"y":984.784,"z":323},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.121"},"t":"word","r":[4]},{"c":"the ","p":{"h":14.199,"w":18.796,"x":730.079,"y":987.258,"z":324},"ps":{"_opacity":1,"_scaleX":0.857},"t":"word","r":[31]},{"c":"R\u201d ","p":{"h":9.21,"w":11.447,"x":186.48,"y":1001.718,"z":233},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[27]},{"c":"gradient ","p":{"h":17.269,"w":58.014,"x":755.64,"y":984.784,"z":325},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[21]},{"c":"converges at every ","p":{"h":17.269,"w":123.058,"x":37.44,"y":1018.984,"z":234},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"0.79"},"t":"word","r":[4]},{"c":"p","p":{"h":17.269,"w":7.134,"x":158.4,"y":1018.984,"z":235},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"oint of continuity of g(X) to ","p":{"h":17.269,"w":183.983,"x":166.564,"y":1018.984,"z":236},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.256"},"t":"word","r":[4]},{"c":"estimate ","p":{"h":17.269,"w":59.037,"x":430.918,"y":1003.144,"z":326},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[19]},{"c":"i","p":{"h":17.269,"w":2.774,"x":487.798,"y":1003.144,"z":327},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"s uniformly consistent. ","p":{"h":17.269,"w":152.706,"x":491.212,"y":1003.144,"z":328},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.091"},"t":"word","r":[4]},{"c":"D. Uniform Consistency ","p":{"h":15.734,"w":154.785,"x":431.28,"y":1034.621,"z":329},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.584"},"t":"word","r":[6]},{"c":"= ","p":{"h":9.21,"w":5.758,"x":194.757,"y":1065.078,"z":239},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.649"},"t":"word","r":[0]},{"c":"dx) ","p":{"h":9.21,"w":11.955,"x":212.036,"y":1065.078,"z":240},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.509"},"t":"word","r":[0]},{"c":"k(Y) dY. ","p":{"h":15.734,"w":57.317,"x":274.32,"y":1056.581,"z":242},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.807"},"t":"word","r":[6]},{"c":"N-t03 ","p":{"h":9.21,"w":19.841,"x":117.36,"y":1074.078,"z":244},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[17]},{"c":"lim ","p":{"h":20.723,"w":23.544,"x":120.6,"y":1055.801,"z":237},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"font-size":"19.44","letter-spacing":"1.023"},"t":"word","r":[1]},{"c":"gNcX) ","p":{"h":9.21,"w":22.117,"x":149.04,"y":1065.078,"z":238},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.62"},"t":"word","r":[0]},{"c":"s ","p":{"h":9.21,"w":5.182,"x":248.754,"y":1074.798,"z":241},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.546"},"t":"word","r":[0]},{"c":"(14) ","p":{"h":17.269,"w":30.213,"x":389.159,"y":1057.864,"z":243},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"The gradient estimate QxpN(X) is uniformly consistent. ","p":{"h":17.269,"w":369.601,"x":445.68,"y":1057.144,"z":330},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.177"},"t":"word","r":[4]},{"c":"R\u201d ","p":{"h":9.21,"w":11.447,"x":257.031,"y":1076.958,"z":245},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[27]},{"c":"That is, for every ","p":{"h":17.269,"w":116.938,"x":430.919,"y":1075.504,"z":331},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[15]},{"c":"F","p":{"h":17.269,"w":7.531,"x":546.12,"y":1075.504,"z":332},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":" > 0, ","p":{"h":17.269,"w":35.716,"x":555.311,"y":1075.504,"z":333},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.039"},"t":"word","r":[4]},{"c":"Using this we will be able to show that the estimate ","p":{"h":17.269,"w":368.279,"x":51.84,"y":1094.584,"z":246},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.671"},"t":"word","r":[4]},{"c":"6,pN(X) is asymptotically unbiased ","p":{"h":17.269,"w":239.176,"x":37.439,"y":1112.584,"z":247},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"font-size":"16.2"},"t":"word","r":[4,29]},{"c":"f","p":{"h":17.269,"w":3.567,"x":273.961,"y":1112.584,"z":248},"ps":{"_opacity":1,"_scaleX":0.906},"t":"word","r":[4]},{"c":"or a class of density ","p":{"h":17.269,"w":140.704,"x":278.4,"y":1112.584,"z":249},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.365"},"t":"word","r":[4]},{"c":"lim Pr {sup II$,pN(X) - V,p(X)ll ","p":{"h":17.269,"w":220.636,"x":470.519,"y":1103.224,"z":334},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"1.687"},"t":"word","r":[4]},{"c":"N-+m ","p":{"h":9.21,"w":19.718,"x":467.64,"y":1121.238,"z":337},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[0,33]},{"c":"R\u201d ","p":{"h":17.269,"w":22.007,"x":531.719,"y":1114.744,"z":338},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"-0.517"},"t":"word","r":[4]},{"c":"> E} = 0. ","p":{"h":17.269,"w":68.667,"x":703.441,"y":1103.224,"z":335},"ps":{"_opacity":1,"_scaleX":0.906},"s":{"letter-spacing":"2.193"},"t":"word","r":[4]},{"c":"(25) ","p":{"h":17.269,"w":30.213,"x":782.641,"y":1103.224,"z":336},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.906},"t":"word","r":[8]},{"c":"Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 29, 2009 at 00:59 from IEEE Xplore.  Restrictions apply. ","p":{"h":9.594,"w":671.742,"x":48.12,"y":1174.884,"z":339},"ps":{"_enter":1},"s":{"font-family":"11b6a7de6f1aff00bed51eac0010002","font-size":"9"},"t":"word","r":[2]}],"page":{"ph":1189.5,"pw":918,"iw":1557,"ih":2166,"v":6,"t":"7","pptlike":false,"cx":0,"cy":0,"cw":915.839,"ch":1187.7}})