]> 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(6).json
Logo AND Algorithmique Numérique Distribuée

Private GIT Repository
initial commit
[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(6).json
1 wenku_8({"font":{"11b6a7de6f1aff00bed51eac0010008":"Helvetica"},"style":[{"t":"style","c":[40,0],"s":{"font-size":"10.44"}},{"t":"style","c":[0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,1],"s":{"font-family":"Arial"}},{"t":"style","c":[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,2],"s":{"color":"#000000"}},{"t":"style","c":[4,20,3],"s":{"font-size":"19.44"}},{"t":"style","c":[4],"s":{"letter-spacing":"1.104"}},{"t":"style","c":[6,8,9,10,11,12,13,14,18,19,23,24,25,29,30,31,33,34,35,36,37,38,5],"s":{"font-size":"14.76"}},{"t":"style","c":[6],"s":{"letter-spacing":"0.955"}},{"t":"style","c":[15,21,22,28,7],"s":{"font-size":"8.64"}},{"t":"style","c":[8],"s":{"letter-spacing":"1.364"}},{"t":"style","c":[9],"s":{"letter-spacing":"0.188"}},{"t":"style","c":[10],"s":{"letter-spacing":"0.731"}},{"t":"style","c":[11],"s":{"letter-spacing":"0.91"}},{"t":"style","c":[12],"s":{"letter-spacing":"1.09"}},{"t":"style","c":[13],"s":{"letter-spacing":"0.682"}},{"t":"style","c":[14],"s":{"letter-spacing":"0.951"}},{"t":"style","c":[15],"s":{"letter-spacing":"0.787"}},{"t":"style","c":[16],"s":{"letter-spacing":"2.991"}},{"t":"style","c":[16,41,17],"s":{"font-size":"46.44"}},{"t":"style","c":[18],"s":{"letter-spacing":"2.097"}},{"t":"style","c":[19],"s":{"letter-spacing":"0.768"}},{"t":"style","c":[20],"s":{"letter-spacing":"1.294"}},{"t":"style","c":[21],"s":{"letter-spacing":"-1.274"}},{"t":"style","c":[22],"s":{"letter-spacing":"0.422"}},{"t":"style","c":[23],"s":{"letter-spacing":"0.82"}},{"t":"style","c":[24],"s":{"letter-spacing":"0.455"}},{"t":"style","c":[25],"s":{"letter-spacing":"0.578"}},{"t":"style","c":[25,26],"s":{"letter-spacing":"0.578"}},{"t":"style","c":[27],"s":{"letter-spacing":"0.262"}},{"t":"style","c":[28],"s":{"letter-spacing":"-0.212"}},{"t":"style","c":[29],"s":{"letter-spacing":"0.841"}},{"t":"style","c":[30],"s":{"letter-spacing":"0.191"}},{"t":"style","c":[31],"s":{"letter-spacing":"1.436"}},{"t":"style","c":[32],"s":{"letter-spacing":"0.73"}},{"t":"style","c":[33],"s":{"letter-spacing":"1.517"}},{"t":"style","c":[34],"s":{"letter-spacing":"0.758"}},{"t":"style","c":[35],"s":{"letter-spacing":"0.894"}},{"t":"style","c":[36],"s":{"letter-spacing":"0.729"}},{"t":"style","c":[37],"s":{"letter-spacing":"1.179"}},{"t":"style","c":[38],"s":{"letter-spacing":"0.813"}},{"t":"style","c":[39],"s":{"letter-spacing":"0.968"}},{"t":"style","c":[40],"s":{"letter-spacing":"0.412"}},{"t":"style","c":[41],"s":{"letter-spacing":"1.495"}}],"body":[{"c":{"ix":0,"iy":0,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":0,"y0":36.72,"y1":0,"y2":0,"y3":36.72,"z":0},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_0.png"},"t":"pic"},{"c":{"ix":0,"iy":67,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":36.72,"y0":73.44,"y1":36.72,"y2":36.72,"y3":73.44,"z":1},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_1.png"},"t":"pic"},{"c":{"ix":0,"iy":134,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":73.44,"y0":110.16,"y1":73.44,"y2":73.44,"y3":110.16,"z":2},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_2.png"},"t":"pic"},{"c":{"ix":0,"iy":201,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":110.159,"y0":146.879,"y1":110.159,"y2":110.159,"y3":146.879,"z":3},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_3.png"},"t":"pic"},{"c":{"ix":0,"iy":268,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":146.879,"y0":183.599,"y1":146.879,"y2":146.879,"y3":183.599,"z":4},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_4.png"},"t":"pic"},{"c":{"ix":0,"iy":335,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":183.599,"y0":220.319,"y1":183.599,"y2":183.599,"y3":220.319,"z":5},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_5.png"},"t":"pic"},{"c":{"ix":0,"iy":402,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":220.319,"y0":257.039,"y1":220.319,"y2":220.319,"y3":257.039,"z":6},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_6.png"},"t":"pic"},{"c":{"ix":0,"iy":469,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":257.039,"y0":293.76,"y1":257.039,"y2":257.039,"y3":293.76,"z":7},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_7.png"},"t":"pic"},{"c":{"ix":0,"iy":536,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":293.759,"y0":330.479,"y1":293.759,"y2":293.759,"y3":330.479,"z":8},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_8.png"},"t":"pic"},{"c":{"ix":0,"iy":603,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":330.479,"y0":367.199,"y1":330.479,"y2":330.479,"y3":367.199,"z":9},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_9.png"},"t":"pic"},{"c":{"ix":0,"iy":670,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":367.199,"y0":403.919,"y1":367.199,"y2":367.199,"y3":403.919,"z":10},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_10.png"},"t":"pic"},{"c":{"ix":0,"iy":737,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":403.919,"y0":440.64,"y1":403.919,"y2":403.919,"y3":440.64,"z":11},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_11.png"},"t":"pic"},{"c":{"ix":0,"iy":804,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":440.64,"y0":477.36,"y1":440.64,"y2":440.64,"y3":477.36,"z":12},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_12.png"},"t":"pic"},{"c":{"ix":0,"iy":871,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":477.36,"y0":514.08,"y1":477.36,"y2":477.36,"y3":514.08,"z":13},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_13.png"},"t":"pic"},{"c":{"ix":0,"iy":938,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":514.079,"y0":550.8,"y1":514.079,"y2":514.079,"y3":550.8,"z":14},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_14.png"},"t":"pic"},{"c":{"ix":0,"iy":1005,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":550.8,"y0":587.52,"y1":550.8,"y2":550.8,"y3":587.52,"z":15},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_15.png"},"t":"pic"},{"c":{"ix":0,"iy":1072,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":587.52,"y0":624.24,"y1":587.52,"y2":587.52,"y3":624.24,"z":16},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_16.png"},"t":"pic"},{"c":{"ix":0,"iy":1139,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":624.24,"y0":660.96,"y1":624.24,"y2":624.24,"y3":660.96,"z":17},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_17.png"},"t":"pic"},{"c":{"ix":0,"iy":1206,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":660.96,"y0":697.68,"y1":660.96,"y2":660.96,"y3":697.68,"z":18},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_18.png"},"t":"pic"},{"c":{"ix":0,"iy":1273,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":697.68,"y0":734.4,"y1":697.68,"y2":697.68,"y3":734.4,"z":19},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_19.png"},"t":"pic"},{"c":{"ix":0,"iy":1340,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":734.4,"y0":771.12,"y1":734.4,"y2":734.4,"y3":771.12,"z":20},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_20.png"},"t":"pic"},{"c":{"ix":0,"iy":1407,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":771.12,"y0":807.84,"y1":771.12,"y2":771.12,"y3":807.84,"z":21},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_21.png"},"t":"pic"},{"c":{"ix":0,"iy":1474,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":807.839,"y0":844.56,"y1":807.839,"y2":807.839,"y3":844.56,"z":22},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_22.png"},"t":"pic"},{"c":{"ix":0,"iy":1541,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":844.56,"y0":881.28,"y1":844.56,"y2":844.56,"y3":881.28,"z":23},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_23.png"},"t":"pic"},{"c":{"ix":0,"iy":1608,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":881.28,"y0":918,"y1":881.28,"y2":881.28,"y3":918,"z":24},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_24.png"},"t":"pic"},{"c":{"ix":0,"iy":1675,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":918,"y0":954.72,"y1":918,"y2":918,"y3":954.72,"z":25},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_25.png"},"t":"pic"},{"c":{"ix":0,"iy":1742,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":954.72,"y0":991.44,"y1":954.72,"y2":954.72,"y3":991.44,"z":26},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_26.png"},"t":"pic"},{"c":{"ix":0,"iy":1809,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":991.44,"y0":1028.16,"y1":991.44,"y2":991.44,"y3":1028.16,"z":27},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_27.png"},"t":"pic"},{"c":{"ix":0,"iy":1876,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":1028.16,"y0":1064.88,"y1":1028.16,"y2":1028.16,"y3":1064.88,"z":28},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_28.png"},"t":"pic"},{"c":{"ix":0,"iy":1943,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":1064.879,"y0":1101.6,"y1":1064.879,"y2":1064.879,"y3":1101.6,"z":29},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_29.png"},"t":"pic"},{"c":{"ix":0,"iy":2010,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":1101.6,"y0":1138.32,"y1":1101.6,"y2":1101.6,"y3":1138.32,"z":30},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_30.png"},"t":"pic"},{"c":{"ix":0,"iy":2077,"iw":1556,"ih":62},"p":{"h":62,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":1138.32,"y0":1175.04,"y1":1138.32,"y2":1138.32,"y3":1175.04,"z":31},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_31.png"},"t":"pic"},{"c":{"ix":0,"iy":2144,"iw":1556,"ih":22},"p":{"h":22,"opacity":1,"rotate":0,"w":915.479,"x":0,"x0":0,"x1":0,"x2":915.479,"x3":915.479,"y":1175.04,"y0":1188,"y1":1175.04,"y2":1175.04,"y3":1188,"z":32},"ps":null,"s":{"pic_file":"\/home\/iknow\/conv\/\/data\/\/bdef\/\/97100832\/\/97100832_8_32.png"},"t":"pic"},{"c":"FUKUNAGA ","p":{"h":11.129,"w":51.208,"x":35.64,"y":28.472,"z":33},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.883"},"t":"word","r":[0]},{"c":"AND HOSTETLER : GRADIENT ","p":{"h":11.129,"w":137.867,"x":96.118,"y":28.472,"z":34},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"1.123"},"t":"word","r":[0]},{"c":"OF DENSITY FUNCTION ","p":{"h":11.129,"w":109.748,"x":241.555,"y":28.472,"z":35},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"1.128"},"t":"word","r":[0]},{"c":"39 ","p":{"h":20.723,"w":22.316,"x":792.36,"y":21.821,"z":36},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.881},"t":"word","r":[4]},{"c":"Now looking at the ith component of this expectation and ","p":{"h":15.734,"w":378.24,"x":35.64,"y":63.641,"z":37},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.69"},"t":"word","r":[5]},{"c":"Using conditions (20)-(22), we see that [k,\u2018(Y)12 satisfies the ","p":{"h":15.734,"w":377.306,"x":429.48,"y":64.361,"z":161},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.114"},"t":"word","r":[5]},{"c":"integrating by parts, ","p":{"h":15.734,"w":121.901,"x":35.64,"y":80.201,"z":38},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[6]},{"c":"conditions needed for (14) to hold. Thus ","p":{"h":15.734,"w":239.656,"x":429.12,"y":80.921,"z":162},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.96"},"t":"word","r":[5]},{"c":"-%(%PNi~))d ","p":{"h":9.21,"w":45.378,"x":34.919,"y":121.458,"z":39},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.605"},"t":"word","r":[7]},{"c":"= -h-\u201d ","p":{"h":15.734,"w":44.745,"x":127.08,"y":116.201,"z":40},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[8]},{"c":"k(h-\u2018(X ","p":{"h":15.734,"w":41.672,"x":216.722,"y":114.401,"z":42},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[9]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":273.243,"y":114.401,"z":43},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y))p(Y) ","p":{"h":15.734,"w":45.15,"x":290.163,"y":114.401,"z":44},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.831"},"t":"word","r":[5]},{"c":"lim h-\u201d ","p":{"h":15.734,"w":49.498,"x":431.64,"y":114.401,"z":163},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.307"},"t":"word","r":[5]},{"c":"a ","p":{"h":15.734,"w":9.848,"x":535.323,"y":106.121,"z":164},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[11]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":182.161,"y":129.521,"z":41},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R\u201d-i ","p":{"h":15.734,"w":24.01,"x":189.001,"y":126.281,"z":47},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-0.058"},"t":"word","r":[5]},{"c":"y*=-CO ","p":{"h":15.734,"w":45.833,"x":345.244,"y":128.081,"z":48},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.998"},"t":"word","r":[5]},{"c":"+* ","p":{"h":15.734,"w":15.141,"x":346.324,"y":114.401,"z":45},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[13]},{"c":"dY ","p":{"h":15.734,"w":18.194,"x":384.485,"y":114.401,"z":46},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[14]},{"c":"N-CO ","p":{"h":9.21,"w":20.648,"x":427.68,"y":130.818,"z":167},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[15]},{"c":"a(h- \u2018zi) ","p":{"h":15.734,"w":48.128,"x":514.799,"y":126.281,"z":168},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.383"},"t":"word","r":[5]},{"c":"k(h-\u2018Z) ","p":{"h":15.734,"w":41.046,"x":566.643,"y":114.401,"z":165},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.214"},"t":"word","r":[5]},{"c":"1 ","p":{"h":49.505,"w":31.467,"x":615.599,"y":102.668,"z":169},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[16]},{"c":"2 p(X - Z) dZ ","p":{"h":15.734,"w":91.729,"x":622.805,"y":114.401,"z":166},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[18]},{"c":"+ h-\u201d ","p":{"h":15.734,"w":38.698,"x":171.721,"y":159.401,"z":49},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.203"},"t":"word","r":[5]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":213.482,"y":174.521,"z":50},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"k(h-l(X ","p":{"h":15.734,"w":41.608,"x":236.16,"y":159.761,"z":53},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[19]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":293.401,"y":159.761,"z":54},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y)) $ ","p":{"h":15.734,"w":33.609,"x":309.961,"y":159.761,"z":55},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[8]},{"c":"p(Y) dY. ","p":{"h":15.734,"w":56.928,"x":354.602,"y":159.761,"z":56},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.639"},"t":"word","r":[5]},{"c":"= P(X) ","p":{"h":15.734,"w":43.409,"x":619.56,"y":161.561,"z":170},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.468"},"t":"word","r":[5]},{"c":"k\u2019O\u2019)12 ","p":{"h":20.723,"w":58.884,"x":695.16,"y":157.541,"z":172},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"-0.408"},"t":"word","r":[3]},{"c":"d","p":{"h":20.723,"w":8.323,"x":750.599,"y":157.541,"z":173},"ps":{"_opacity":1,"_scaleX":0.881},"t":"word","r":[3]},{"c":"Y ","p":{"h":20.723,"w":14.25,"x":760.216,"y":157.541,"z":174},"ps":{"_opacity":1,"_scaleX":0.881},"t":"word","r":[20]},{"c":"R","p":{"h":9.21,"w":4.557,"x":220.32,"y":178.698,"z":51},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[7]},{"c":"\u201d ","p":{"h":9.21,"w":6.166,"x":225.726,"y":178.698,"z":52},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[21]},{"c":"1 ","p":{"h":9.21,"w":5.666,"x":347.76,"y":178.698,"z":57},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[22]},{"c":"WI ","p":{"h":15.734,"w":18.194,"x":387.719,"y":189.641,"z":58},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[14]},{"c":"which is finite. Substituting (77), (76), an: (74) into (73) and ","p":{"h":15.734,"w":377.881,"x":428.392,"y":187.481,"z":176},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.29"},"t":"word","r":[5]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":669.601,"y":174.521,"z":171},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"(77) ","p":{"h":15.734,"w":26.416,"x":781.199,"y":161.561,"z":175},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"Since k(Y) is bounded, from (2), and p(X) is a probability ","p":{"h":15.734,"w":372.749,"x":35.632,"y":212.681,"z":59},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.578"},"t":"word","r":[5]},{"c":"using condition (19) on h(N), we obtain ","p":{"h":15.734,"w":234.315,"x":428.752,"y":204.041,"z":177},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.001"},"t":"word","r":[5]},{"c":"density function with (15) satisfied, the first term of (68) is ","p":{"h":15.734,"w":378.055,"x":35.632,"y":228.881,"z":60},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.452"},"t":"word","r":[5]},{"c":"zero as ","p":{"h":15.734,"w":45.995,"x":35.272,"y":245.441,"z":61},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.961"},"t":"word","r":[5]},{"c":"N-02 ","p":{"h":9.21,"w":17.595,"x":472.68,"y":245.658,"z":181},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.548"},"t":"word","r":[7]},{"c":"lia ","p":{"h":20.723,"w":20.735,"x":476.64,"y":227.381,"z":178},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"0.656"},"t":"word","r":[3]},{"c":"EIll~x~~(X) ","p":{"h":11.129,"w":47.045,"x":502.56,"y":235.112,"z":179},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.584"},"t":"word","r":[0]},{"c":"- V,P(-JOII~~ ","p":{"h":20.723,"w":110.323,"x":583.92,"y":227.381,"z":180},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"1.516"},"t":"word","r":[3]},{"c":",;rnm jk(h-l(X ","p":{"h":15.734,"w":81.788,"x":43.552,"y":271.361,"z":62},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.039"},"t":"word","r":[5]},{"c":"i\u2019 ","p":{"h":15.734,"w":13.485,"x":51.472,"y":283.601,"z":69},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-1.837"},"t":"word","r":[5]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":140.394,"y":271.361,"z":63},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y))p(Y)j ","p":{"h":15.734,"w":47.898,"x":157.315,"y":271.361,"z":64},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.751"},"t":"word","r":[5]},{"c":"I ","p":{"h":15.734,"w":6.737,"x":217.436,"y":271.361,"z":65},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"sup [k(Y)] ","p":{"h":15.734,"w":63.173,"x":236.156,"y":271.361,"z":66},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.24"},"t":"word","r":[5]},{"c":"lim ","p":{"h":15.734,"w":18.8,"x":310.318,"y":271.361,"z":67},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"p(Y) = 0. ","p":{"h":15.734,"w":65.573,"x":339.839,"y":271.361,"z":68},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.182"},"t":"word","r":[5]},{"c":"YER\u201d ","p":{"h":9.21,"w":21.373,"x":233.28,"y":287.418,"z":70},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[7,27]},{"c":"1yi1-m ","p":{"h":9.21,"w":23.616,"x":303.475,"y":288.498,"z":71},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.501"},"t":"word","r":[7]},{"c":"= ig [ik ","p":{"h":20.723,"w":61.056,"x":489.24,"y":269.861,"z":182},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"1.874"},"t":"word","r":[3]},{"c":"Wh\u201d+2Y-1p(x> ","p":{"h":20.723,"w":115.105,"x":564.118,"y":269.861,"z":183},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"0.913"},"t":"word","r":[3]},{"c":"1 ","p":{"h":20.723,"w":12.888,"x":660.597,"y":269.861,"z":184},"ps":{"_opacity":1,"_scaleX":0.881},"t":"word","r":[4]},{"c":"k\u2019(Y)12 ","p":{"h":20.723,"w":58.579,"x":686.156,"y":269.861,"z":185},"ps":{"_opacity":1,"_scaleX":0.881},"s":{"letter-spacing":"0.352"},"t":"word","r":[3]},{"c":"d","p":{"h":20.723,"w":8.323,"x":740.875,"y":269.861,"z":186},"ps":{"_opacity":1,"_scaleX":0.881},"t":"word","r":[3]},{"c":"Y ","p":{"h":20.723,"w":14.25,"x":750.493,"y":269.861,"z":187},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.881},"t":"word","r":[20]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":667.8,"y":290.658,"z":188},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"(6% ","p":{"h":9.21,"w":14.588,"x":387.71,"y":308.298,"z":72},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.613"},"t":"word","r":[7]},{"c":"Under the conditions (2)-(6), we can apply (14) to obtain the ","p":{"h":15.734,"w":377.666,"x":35.64,"y":325.721,"z":73},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.28"},"t":"word","r":[5]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":506.879,"y":325.361,"z":189},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"lim N-\u2019 $ ","p":{"h":15.734,"w":68.529,"x":525.24,"y":325.361,"z":190},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.761"},"t":"word","r":[5]},{"c":"p(X) ","p":{"h":15.734,"w":27.532,"x":604.442,"y":325.361,"z":191},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[29]},{"c":"= 0. ","p":{"h":15.734,"w":29.572,"x":649.083,"y":325.361,"z":192},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.951"},"t":"word","r":[5]},{"c":"(78) ","p":{"h":15.734,"w":26.416,"x":780.839,"y":327.521,"z":194},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"second ","p":{"h":15.734,"w":44.993,"x":35.639,"y":342.641,"z":74},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.97"},"t":"word","r":[5]},{"c":"t","p":{"h":15.734,"w":3.17,"x":79.2,"y":342.641,"z":75},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"erm ","p":{"h":15.734,"w":24.616,"x":83.234,"y":342.641,"z":76},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.862"},"t":"word","r":[5]},{"c":"N+CO ","p":{"h":9.21,"w":22.25,"x":521.64,"y":341.778,"z":195},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.793"},"t":"word","r":[7]},{"c":"i ","p":{"h":15.734,"w":6.067,"x":598.68,"y":339.401,"z":196},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[30]},{"c":"1 ","p":{"h":49.505,"w":31.467,"x":635.4,"y":313.628,"z":193},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[16]},{"c":"lim h-\u201d ","p":{"h":15.734,"w":49.138,"x":38.159,"y":376.121,"z":77},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.255"},"t":"word","r":[5]},{"c":"k(h-\u2018(X ","p":{"h":15.734,"w":41.672,"x":113.039,"y":376.481,"z":82},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[9]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":169.921,"y":376.481,"z":83},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y)) $ ","p":{"h":15.734,"w":33.969,"x":186.841,"y":376.481,"z":84},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[31]},{"c":"p(Y) dY ","p":{"h":15.734,"w":52.754,"x":231.482,"y":376.481,"z":85},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.756"},"t":"word","r":[5]},{"c":"C. Uniform Consistency ","p":{"h":15.734,"w":146.186,"x":429.116,"y":371.801,"z":197},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.175"},"t":"word","r":[5]},{"c":"N-rCO ","p":{"h":9.21,"w":23.397,"x":34.56,"y":392.538,"z":78},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"font-size":"8.64"},"t":"word","r":[7,32]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":90.72,"y":391.601,"z":79},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R","p":{"h":9.21,"w":4.557,"x":97.56,"y":395.778,"z":80},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[7]},{"c":"\u201d ","p":{"h":9.21,"w":6.166,"x":102.966,"y":395.778,"z":81},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[21]},{"c":"1 ","p":{"h":9.21,"w":5.666,"x":225.359,"y":396.138,"z":86},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[22]},{"c":"In this section we will show that the gradient estimate is ","p":{"h":15.734,"w":364.734,"x":441.716,"y":394.481,"z":198},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[33]},{"c":"= $P(X) ","p":{"h":15.734,"w":51.731,"x":155.88,"y":419.681,"z":87},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.542"},"t":"word","r":[5]},{"c":"i ","p":{"h":15.734,"w":6.067,"x":186.48,"y":431.561,"z":88},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[30]},{"c":"k(Y) dY = $ ","p":{"h":15.734,"w":83.29,"x":250.2,"y":417.521,"z":92},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.295"},"t":"word","r":[5]},{"c":"p(X) ","p":{"h":15.734,"w":27.532,"x":344.161,"y":417.521,"z":93},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[29]},{"c":"(70) ","p":{"h":15.734,"w":26.416,"x":387.722,"y":417.521,"z":94},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"uniformly consistent in probability; that is, ","p":{"h":15.734,"w":256.108,"x":428.396,"y":411.041,"z":199},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.065"},"t":"word","r":[5]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":227.881,"y":433.001,"z":89},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R","p":{"h":9.21,"w":4.557,"x":234.72,"y":436.818,"z":90},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[7]},{"c":"\u201d ","p":{"h":9.21,"w":6.166,"x":240.126,"y":436.818,"z":91},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[21]},{"c":"1 ","p":{"h":9.21,"w":5.666,"x":338.4,"y":436.818,"z":95},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[22]},{"c":"where the last equality follows from condition (5) on k(X). ","p":{"h":15.734,"w":347.128,"x":35.64,"y":454.241,"z":96},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.066"},"t":"word","r":[5]},{"c":"N-PLO ","p":{"h":9.21,"w":24.243,"x":474.12,"y":452.658,"z":205},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.692"},"t":"word","r":[7]},{"c":"lim pr {,\u201cwn ","p":{"h":15.734,"w":76.88,"x":477.717,"y":438.761,"z":200},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.36"},"t":"word","r":[5]},{"c":"II~xPN(x) ","p":{"h":9.21,"w":33.303,"x":560.52,"y":444.018,"z":201},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.559"},"t":"word","r":[7]},{"c":"- vd(x)ll ","p":{"h":15.734,"w":53.907,"x":623.52,"y":438.761,"z":202},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.567"},"t":"word","r":[5]},{"c":"\u2019 &) = 0. ","p":{"h":15.734,"w":62.333,"x":697.681,"y":438.761,"z":203},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.327"},"t":"word","r":[5]},{"c":"(79 ","p":{"h":15.734,"w":21.775,"x":780.483,"y":438.401,"z":204},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.85"},"t":"word","r":[5]},{"c":"Asymptotic ","p":{"h":15.734,"w":66.164,"x":48.96,"y":470.801,"z":97},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.854"},"t":"word","r":[5]},{"c":"unbiasedness (16) now follows by substituting ","p":{"h":15.734,"w":287.263,"x":124.201,"y":470.801,"z":98},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.246"},"t":"word","r":[5]},{"c":"To show this, we notice that the gradient estimate is the ","p":{"h":15.734,"w":364.346,"x":441.719,"y":470.081,"z":206},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.523"},"t":"word","r":[5]},{"c":"(69) and (70) in the limit of (68). ","p":{"h":15.734,"w":195.008,"x":35.64,"y":487.001,"z":99},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.003"},"t":"word","r":[5]},{"c":"convolution ","p":{"h":15.734,"w":68.666,"x":428.039,"y":486.641,"z":207},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.771"},"t":"word","r":[5]},{"c":"of ","p":{"h":15.734,"w":13.732,"x":511.921,"y":486.641,"z":208},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[13]},{"c":"the ","p":{"h":15.734,"w":20.898,"x":537.482,"y":486.641,"z":209},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[34]},{"c":"sample ","p":{"h":15.734,"w":44.27,"x":569.882,"y":486.641,"z":210},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[35]},{"c":"function ","p":{"h":15.734,"w":48.448,"x":623.884,"y":486.641,"z":211},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[36]},{"c":"and ","p":{"h":15.734,"w":24.353,"x":686.525,"y":486.641,"z":212},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[11]},{"c":"the ","p":{"h":15.734,"w":20.898,"x":722.526,"y":486.641,"z":213},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[34]},{"c":"function ","p":{"h":15.734,"w":48.448,"x":754.207,"y":486.641,"z":214},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[36]},{"c":"B. Consistency ","p":{"h":15.734,"w":94.345,"x":35.28,"y":514.001,"z":100},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.193"},"t":"word","r":[5]},{"c":"h-\u201cV,k(h-lx). ","p":{"h":15.734,"w":71.75,"x":427.679,"y":503.201,"z":215},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.507"},"t":"word","r":[5]},{"c":"Applying the properties of Fourier transforms, ","p":{"h":15.734,"w":283.433,"x":521.642,"y":503.201,"z":216},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.19"},"t":"word","r":[5]},{"c":"we see ","p":{"h":15.734,"w":44.641,"x":428.04,"y":519.401,"z":217},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.158"},"t":"word","r":[5]},{"c":"t","p":{"h":15.734,"w":3.17,"x":470.881,"y":519.401,"z":218},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"hat the Fourier transform of qxpN(X) is the product of ","p":{"h":15.734,"w":330.285,"x":474.734,"y":519.401,"z":219},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.194"},"t":"word","r":[5]},{"c":"In this section we will show that the gradient estimate is ","p":{"h":15.734,"w":364.734,"x":48.6,"y":536.321,"z":101},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[33]},{"c":"the Fourier transforms of the sample function and that of ","p":{"h":15.734,"w":376.62,"x":428.04,"y":535.961,"z":220},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.662"},"t":"word","r":[5]},{"c":"consistent in a mean-square ","p":{"h":15.734,"w":168.352,"x":34.92,"y":552.881,"z":102},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.899"},"t":"word","r":[5]},{"c":"s","p":{"h":15.734,"w":5.637,"x":201.963,"y":552.881,"z":103},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"ense; ","p":{"h":15.734,"w":34.921,"x":208.495,"y":552.881,"z":104},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[35]},{"c":"t","p":{"h":15.734,"w":3.17,"x":241.204,"y":552.881,"z":105},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"hat is, ","p":{"h":15.734,"w":39.49,"x":245.058,"y":552.881,"z":106},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.933"},"t":"word","r":[5]},{"c":"h-\u201cV,k(h-IX). ","p":{"h":15.734,"w":74.363,"x":427.68,"y":552.521,"z":221},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.52"},"t":"word","r":[5]},{"c":"Using the inversion relationship, we see ","p":{"h":15.734,"w":240.846,"x":520.562,"y":552.521,"z":222},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.015"},"t":"word","r":[5]},{"c":"t","p":{"h":15.734,"w":3.17,"x":759.607,"y":552.521,"z":223},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"hat ","p":{"h":15.734,"w":20.756,"x":763.461,"y":552.521,"z":224},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[13]},{"c":"E{lt%,pN(X) ","p":{"h":9.21,"w":41.236,"x":34.919,"y":585.498,"z":107},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.567"},"t":"word","r":[7]},{"c":"- v,p(x>I12) = E{ll~x,pN(X) - E@dd~)~l12~ ","p":{"h":15.734,"w":276.811,"x":113.399,"y":580.241,"z":108},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.539"},"t":"word","r":[5]},{"c":"f&(x) ","p":{"h":15.734,"w":30.681,"x":428.04,"y":586.721,"z":225},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.8"},"t":"word","r":[5]},{"c":"= (2$-l ","p":{"h":15.734,"w":43.977,"x":485.281,"y":586.721,"z":226},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.262"},"t":"word","r":[5]},{"c":"exp ( -jWTX>@N(W) [ -jWK(hW)] ","p":{"h":15.734,"w":197.455,"x":564.483,"y":586.361,"z":228},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.069"},"t":"word","r":[5]},{"c":"dW ","p":{"h":15.734,"w":21.562,"x":784.088,"y":586.361,"z":229},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[37]},{"c":"+ ","p":{"h":15.734,"w":10.213,"x":216.362,"y":606.161,"z":109},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[38]},{"c":"llE{~xPN(x)) ","p":{"h":9.21,"w":42.58,"x":234.359,"y":611.418,"z":110},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.547"},"t":"word","r":[7]},{"c":"- VXP(~)II~ ","p":{"h":15.734,"w":75.247,"x":316.799,"y":606.161,"z":111},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.467"},"t":"word","r":[5]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":542.523,"y":601.481,"z":227},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":549.36,"y":605.298,"z":230},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"(71) ","p":{"h":15.734,"w":26.416,"x":388.081,"y":627.401,"z":112},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"030) ","p":{"h":15.734,"w":29.01,"x":780.12,"y":615.521,"z":231},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.865"},"t":"word","r":[5]},{"c":"goes to zero as N approaches infinity. ","p":{"h":15.734,"w":238.226,"x":35.633,"y":650.801,"z":113},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.282"},"t":"word","r":[5]},{"c":"Since the estimate is ","p":{"h":15.734,"w":130.369,"x":282.959,"y":650.801,"z":114},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.165"},"t":"word","r":[5]},{"c":"where W is an n-dimensional vector, ","p":{"h":15.734,"w":216.418,"x":427.672,"y":639.641,"z":232},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[5,39]},{"c":"asymptotically unbiased for a density function that satisfies ","p":{"h":15.734,"w":351.407,"x":34.913,"y":667.361,"z":115},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.934"},"t":"word","r":[5]},{"c":"(","p":{"h":15.734,"w":3.875,"x":384.121,"y":667.361,"z":116},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"15), ","p":{"h":15.734,"w":25.501,"x":388.744,"y":667.361,"z":117},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.747"},"t":"word","r":[5]},{"c":"@N(w) ","p":{"h":9.21,"w":24.999,"x":526.319,"y":680.178,"z":233},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.786"},"t":"word","r":[7]},{"c":"= $ & ","p":{"h":15.734,"w":41.855,"x":574.2,"y":674.921,"z":234},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.723"},"t":"word","r":[5]},{"c":"\u2018exp (,iWT&) ","p":{"h":15.734,"w":73.118,"x":626.041,"y":674.921,"z":235},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.401"},"t":"word","r":[5]},{"c":"(81) ","p":{"h":15.734,"w":26.416,"x":780.124,"y":674.921,"z":237},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"N-CO ","p":{"h":9.21,"w":20.648,"x":110.16,"y":708.978,"z":124},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[15]},{"c":"lim ","p":{"h":15.734,"w":18.8,"x":113.755,"y":695.081,"z":118},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[25]},{"c":"jlE{~x,pN(X)} ","p":{"h":9.21,"w":45.034,"x":141.84,"y":700.338,"z":119},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.524"},"t":"word","r":[7]},{"c":"- ~x,P(~)~~~ ","p":{"h":15.734,"w":84.053,"x":227.16,"y":695.081,"z":120},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[31]},{"c":"=","p":{"h":15.734,"w":6.694,"x":307.081,"y":695.081,"z":121},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":" O* ","p":{"h":15.734,"w":25.54,"x":314.589,"y":695.081,"z":122},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.45"},"t":"word","r":[5]},{"c":"(72) ","p":{"h":15.734,"w":26.416,"x":387.363,"y":695.081,"z":123},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"is the sample characteristic function, ","p":{"h":15.734,"w":213.032,"x":427.676,"y":710.561,"z":236},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.762"},"t":"word","r":[5]},{"c":"Substituting (9), the first term of (71) becomes ","p":{"h":15.734,"w":276.849,"x":35.28,"y":727.121,"z":125},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[6]},{"c":"K(W) ","p":{"h":15.734,"w":32.146,"x":511.918,"y":745.121,"z":238},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.976"},"t":"word","r":[5]},{"c":"= ","p":{"h":15.734,"w":10.213,"x":553.679,"y":745.121,"z":239},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[38]},{"c":"exp (jWTX)k(X) ","p":{"h":15.734,"w":91.953,"x":592.92,"y":744.041,"z":241},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.914"},"t":"word","r":[5]},{"c":"dX ","p":{"h":15.734,"w":18.194,"x":701.282,"y":744.041,"z":242},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[14]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":570.239,"y":759.521,"z":240},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"(82) ","p":{"h":15.734,"w":26.416,"x":779.764,"y":745.841,"z":243},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":577.439,"y":763.338,"z":244},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"h-\u2018$ ","p":{"h":15.734,"w":24.535,"x":203.403,"y":785.801,"z":126},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"-0.328"},"t":"word","r":[5]},{"c":"k(h-l(X ","p":{"h":15.734,"w":41.608,"x":249.124,"y":785.801,"z":127},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[19]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":306.366,"y":785.801,"z":128},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"y)) 2 ","p":{"h":15.734,"w":36.129,"x":324.366,"y":785.801,"z":129},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.227"},"t":"word","r":[5]},{"c":"is the characteristic function of k(X), and -jWK(h ","p":{"h":15.734,"w":306.823,"x":427.68,"y":781.121,"z":245},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.34"},"t":"word","r":[5]},{"c":"W) is the ","p":{"h":15.734,"w":60.139,"x":745.207,"y":781.121,"z":246},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.519"},"t":"word","r":[5]},{"c":"i ","p":{"h":11.129,"w":4.182,"x":242.64,"y":803.912,"z":130},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.311"},"t":"word","r":[0]},{"c":"characteristic function of h-\u201cV,k(h-lx) ","p":{"h":15.734,"w":218.212,"x":427.32,"y":797.681,"z":247},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.809"},"t":"word","r":[5]},{"c":"as in (28). Therefore, ","p":{"h":15.734,"w":125.587,"x":666.365,"y":797.681,"z":248},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.804"},"t":"word","r":[5]},{"c":"- E2 ","p":{"h":15.734,"w":34.034,"x":111.96,"y":831.521,"z":132},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.767"},"t":"word","r":[5]},{"c":"h-\u201c$ ","p":{"h":15.734,"w":25.975,"x":157.681,"y":831.521,"z":133},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.031"},"t":"word","r":[5]},{"c":"E\u2019S;! ","p":{"h":11.129,"w":21.024,"x":433.799,"y":829.112,"z":249},"ps":{"_opacity":1,"_scaleX":0.859},"t":"word","r":[0]},{"c":"II~~PN(X) ","p":{"h":11.129,"w":42.145,"x":476.639,"y":829.112,"z":250},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.634"},"t":"word","r":[0]},{"c":"- ","p":{"h":11.129,"w":5.134,"x":539.277,"y":829.112,"z":251},"ps":{"_opacity":1,"_scaleX":0.859},"t":"word","r":[40]},{"c":"E{~x~~(X)III ","p":{"h":11.129,"w":51.192,"x":555.117,"y":829.112,"z":252},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"font-size":"10.44"},"t":"word","r":[0,26]},{"c":"1 ","p":{"h":11.129,"w":6.78,"x":637.555,"y":829.112,"z":253},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.715"},"t":"word","r":[0]},{"c":"i ","p":{"h":15.734,"w":6.067,"x":197.281,"y":845.201,"z":137},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[30]},{"c":"k(h-l(X ","p":{"h":15.734,"w":41.608,"x":203.762,"y":831.521,"z":134},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[19]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":260.643,"y":831.521,"z":135},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y)) . ","p":{"h":15.734,"w":44.178,"x":278.643,"y":831.521,"z":136},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"4.009"},"t":"word","r":[5]},{"c":"From (16), we have ","p":{"h":15.734,"w":118.512,"x":47.879,"y":868.241,"z":139},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.086"},"t":"word","r":[5]},{"c":"II ","p":{"h":49.505,"w":33.137,"x":298.44,"y":819.428,"z":138},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[41]},{"c":"II ","p":{"h":49.505,"w":33.137,"x":343.44,"y":774.428,"z":131},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[41]},{"c":"5 (2$-l ","p":{"h":15.734,"w":45.057,"x":449.28,"y":865.361,"z":254},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.482"},"t":"word","r":[5]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":507.961,"y":880.481,"z":255},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"11 WK(hW)IIE{I@N(W) ","p":{"h":11.129,"w":89.488,"x":532.8,"y":870.152,"z":256},"ps":{"_opacity":1,"_scaleX":0.859},"t":"word","r":[40]},{"c":"- ","p":{"h":11.129,"w":5.134,"x":668.516,"y":870.152,"z":257},"ps":{"_opacity":1,"_scaleX":0.859},"t":"word","r":[40]},{"c":"E{@NW)III ","p":{"h":11.129,"w":45.451,"x":684.356,"y":870.152,"z":258},"ps":{"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.685"},"t":"word","r":[0]},{"c":"dW ","p":{"h":11.129,"w":14.974,"x":761.754,"y":870.152,"z":259},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"font-size":"10.44"},"t":"word","r":[0,39]},{"c":"R\u201d ","p":{"h":11.129,"w":13.916,"x":515.16,"y":882.752,"z":260},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"-0.42"},"t":"word","r":[0]},{"c":"h-\u201d &k(h-l(X ","p":{"h":15.734,"w":74.45,"x":135.722,"y":902.081,"z":140},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.63"},"t":"word","r":[5]},{"c":"(74) ","p":{"h":15.734,"w":26.416,"x":386.647,"y":903.881,"z":143},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"Now ","p":{"h":15.734,"w":28.324,"x":34.199,"y":929.441,"z":145},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.149"},"t":"word","r":[5]},{"c":"I ","p":{"h":15.734,"w":6.737,"x":175.322,"y":915.761,"z":144},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":238.684,"y":902.081,"z":141},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y)) ","p":{"h":15.734,"w":20.306,"x":255.604,"y":902.081,"z":142},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.818"},"t":"word","r":[5]},{"c":"(83) ","p":{"h":15.734,"w":26.416,"x":779.4,"y":898.841,"z":261},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"I (27$-l ","p":{"h":15.734,"w":51.909,"x":449.272,"y":926.921,"z":262},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.697"},"t":"word","r":[5]},{"c":"II ","p":{"h":49.505,"w":33.137,"x":213.48,"y":951.548,"z":151},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[41]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":507.953,"y":942.041,"z":263},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"11 ","p":{"h":15.734,"w":17.1,"x":532.794,"y":927.281,"z":264},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[11]},{"c":"WK(h W)jl var {@#\u2018))\u201c2 ","p":{"h":15.734,"w":142.086,"x":539.634,"y":927.281,"z":265},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.869"},"t":"word","r":[5]},{"c":"dW ","p":{"h":15.734,"w":21.562,"x":701.998,"y":927.281,"z":266},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[37]},{"c":"(84) ","p":{"h":15.734,"w":26.416,"x":779.759,"y":928.001,"z":267},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":515.159,"y":945.858,"z":268},"ps":{"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"E ","p":{"h":15.734,"w":10.894,"x":42.839,"y":963.641,"z":146},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.993"},"t":"word","r":[5]},{"c":"h-\u201c$, ","p":{"h":15.734,"w":29.859,"x":73.44,"y":963.641,"z":147},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.116"},"t":"word","r":[5]},{"c":"k(h-l(X ","p":{"h":15.734,"w":41.608,"x":119.161,"y":963.641,"z":148},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[19]},{"c":"- ","p":{"h":15.734,"w":7.405,"x":176.042,"y":963.641,"z":149},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[10]},{"c":"Y)) 2 ","p":{"h":15.734,"w":37.929,"x":192.963,"y":963.641,"z":150},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"2.228"},"t":"word","r":[5]},{"c":"= (2$1 ","p":{"h":15.734,"w":44.851,"x":448.919,"y":971.921,"z":269},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.65"},"t":"word","r":[5]},{"c":"II ","p":{"h":15.734,"w":10.363,"x":532.801,"y":971.561,"z":271},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"W","p":{"h":15.734,"w":10.569,"x":539.641,"y":971.561,"z":272},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"K(hW)II [N-l ","p":{"h":15.734,"w":76.116,"x":551.108,"y":971.561,"z":273},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"1.217"},"t":"word","r":[5]},{"c":"var {exp (jWTX)}]1\u20192 ","p":{"h":15.734,"w":122.313,"x":639.364,"y":971.561,"z":274},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[34]},{"c":"dW ","p":{"h":15.734,"w":21.562,"x":774.727,"y":971.561,"z":275},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[37]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":507.961,"y":987.401,"z":270},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":514.799,"y":991.218,"z":276},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"h-2nin ","p":{"h":15.734,"w":39.04,"x":74.88,"y":1009.721,"z":152},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.76"},"t":"word","r":[5]},{"c":"[&k(h-?Z)]2p(X- ","p":{"h":15.734,"w":93.364,"x":131.041,"y":1009.721,"z":153},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.83"},"t":"word","r":[5]},{"c":"Z)dZ ","p":{"h":15.734,"w":30.093,"x":268.564,"y":1009.721,"z":154},"ps":{"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.997"},"t":"word","r":[5]},{"c":"(75) ","p":{"h":15.734,"w":26.416,"x":386.639,"y":1010.441,"z":159},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"(85) ","p":{"h":15.734,"w":26.416,"x":779.039,"y":1005.041,"z":277},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"II ","p":{"h":15.734,"w":10.363,"x":532.434,"y":1033.481,"z":281},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"W","p":{"h":15.734,"w":10.569,"x":538.554,"y":1033.481,"z":282},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[5]},{"c":"K(hW)IIN-1\u20192 ","p":{"h":15.734,"w":78.569,"x":550.041,"y":1033.481,"z":283},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.517"},"t":"word","r":[5]},{"c":"dW ","p":{"h":15.734,"w":21.562,"x":643.677,"y":1033.481,"z":284},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[37]},{"c":"(86) ","p":{"h":15.734,"w":26.416,"x":779.4,"y":1034.561,"z":285},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"k(h-\u20182) ","p":{"h":15.734,"w":40.579,"x":238.323,"y":1054.361,"z":155},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"letter-spacing":"0.177"},"t":"word","r":[5]},{"c":"1 ","p":{"h":49.505,"w":31.467,"x":287.28,"y":1041.908,"z":157},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.895},"t":"word","r":[16]},{"c":"I ","p":{"h":15.734,"w":6.737,"x":448.912,"y":1033.841,"z":278},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"(27$-l ","p":{"h":15.734,"w":36.428,"x":464.753,"y":1033.841,"z":279},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"s":{"font-size":"14.76"},"t":"word","r":[5,32]},{"c":"2 p(X - Z) dZ ","p":{"h":15.734,"w":91.729,"x":294.844,"y":1054.361,"z":156},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[18]},{"c":". ","p":{"h":15.734,"w":6.737,"x":396,"y":1054.001,"z":158},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[24]},{"c":"s ","p":{"h":15.734,"w":9.12,"x":507.953,"y":1048.961,"z":280},"ps":{"_opacity":1,"_scaleX":0.884},"t":"word","r":[12]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":514.799,"y":1052.778,"z":286},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"c":"= ","p":{"h":9.21,"w":5.846,"x":448.563,"y":1079.778,"z":287},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.525"},"t":"word","r":[7]},{"c":"(2#\/2hN+\u2018)-1 ","p":{"h":9.21,"w":43.246,"x":464.403,"y":1079.778,"z":288},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.282"},"t":"word","r":[7]},{"c":"(76) ","p":{"h":15.734,"w":26.416,"x":386.279,"y":1092.521,"z":160},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"II -J\u2019WKW) ","p":{"h":11.129,"w":43.989,"x":590.04,"y":1083.992,"z":290},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"font-size":"10.44"},"t":"word","r":[0,27]},{"c":"II dW. ","p":{"h":11.129,"w":27.828,"x":664.198,"y":1083.992,"z":291},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.859},"s":{"letter-spacing":"0.982"},"t":"word","r":[0]},{"c":"(87) ","p":{"h":15.734,"w":26.416,"x":779.4,"y":1079.561,"z":292},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.884},"t":"word","r":[23]},{"c":"s ","p":{"h":9.21,"w":5.244,"x":565.197,"y":1099.218,"z":289},"ps":{"_opacity":1,"_scaleX":0.849},"s":{"letter-spacing":"0.568"},"t":"word","r":[7]},{"c":"R\u201d ","p":{"h":9.21,"w":11.573,"x":572.4,"y":1097.778,"z":293},"ps":{"_enter":1,"_opacity":1,"_scaleX":0.849},"t":"word","r":[28]},{"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":294},"ps":{"_enter":1},"s":{"font-family":"11b6a7de6f1aff00bed51eac0010008","font-size":"9"},"t":"word","r":[2]}],"page":{"ph":1188,"pw":915,"iw":1556,"ih":2166,"v":6,"t":"7","pptlike":false,"cx":0,"cy":0,"cw":915,"ch":1188}})