統(tǒng)計(jì)學(xué)bootstrap

1、1編輯ppt2編輯ppt3編輯ppt()1,.,nnTg XX=nTnT( )FnTV( )FnTV( )FnTV( )nnFTV11nniiTnX-=( )2FnTns=V()( )( )22,xdF xxdF xsmm=-=蝌( )2nnFTns=V()221nniiXXns=-( )FnTV4編輯ppt5編輯ppt6編輯ppt()1,.,nXXX=()1*,.,nbXXX=()12345,XXXXXX=()*123545,XXXXXX=()*213145,XXXXXX=7編輯ppt1 n1,.,nii()*1,.,iinXXX=8編輯ppt()11,1,.10.368njiXXjnen-

2、驏=-換桫PiX9編輯ppt()( ),11BPnn bnnbTTtdGtTB=EnT,1,.,nn BTTnT( )nTEnT( )nTEnGnGB10編輯ppt()()()( )(),11BPn bnnbh Th t dGth TB=E()()()( )22,11BPn bnnnnbTTTTTB=-=EV( )nTV()()2,n bn bnh TTT=-B11編輯ppt1*,.,nXX()1*,.,nnTg XX=1*,.,nnXXFnTnFnFnFnF1,.,nXX12編輯ppt()1,.,nXXX=( )()1,.,nnTgg XX=X( )* ,1111BBn bootn bbbb

3、TTgBB=邋X( )(),1,*,.,n bbn bbTg Xg XX=()1,*,.,bn bbXXX=1,.,bB=13編輯pptX = (3.12, 0, 1.57, 19.67, 0.22, 2.20)Mean=4.46X1=(1.57,0.22,19.67, 0,0,2.2,3.12)Mean=4.13X2=(0, 2.20, 2.20, 2.20, 19.67, 1.57)Mean=4.64X3=(0.22, 3.12,1.57, 3.12, 2.20, 0.22)Mean=1.74()14.134.641.743.503bootMean=+=14編輯ppt()()22,TTnt

4、dGtsm=-( )2FnTTns=V()TntdGtm=( )()2*,1111, nBBnn bnnn bFbbTTTTTBB=-=邋V( )FnTV( )nnFTV( )nnFTVnF15編輯ppt（大數(shù)定律）2*,1111Bnbootn bn rbrvTTBB=驏=-桫邋（計(jì)算boostrap樣本）（計(jì)算boostrap復(fù)制）*1,.,nnXXF:()*1,.,nnTg XX=*,1,.,nn BTT16編輯ppt( )()()2: 0.21,20.86,1FF XNN=+5,m=()1100,.,XXX=4.997,nX =( )()2221 nniniXXXns=-V直接用嵌入式估

5、計(jì)結(jié)果：0.0484=7.0411 4.8397 5.3156 6.7719 7.06165.2546 7.3937 4.3376 4.4010 5.17247.4199 5.3677 6.7028 6.2003 7.57074.1230 3.8914 5.2323 5.5942 7.14793.6790 0.3509 1.4197 1.7X =585 2.4476-3.8635 2.5731 -0.7367 0.5627 1.6379-0.1864 2.7004 2.1487 2.3513 1.4833-1.0138 4.9794 0.1518 2.8683 1.62696.9523 5.3

6、073 4.7191 5.4374 4.61086.5975 6.3495 7.2762 5.9453 4.69936.1559 5.8950 5.7591 5.2173 4.99804.5010 4.7860 5.4382 4.8893 7.29405.5741 5.5139 5.8869 7.2756 5.84496.6439 4.5224 5.5028 4.5672 5.87186.0919 7.1912 6.4181 7.2248 8.41537.3199 5.1305 6.8719 5.2686 5.80555.3602 6.4120 6.0721 5.2740 7.23297.09

7、12 7.0766 5.9750 6.6091 7.21354.9585 5.9042 5.9273 6.5762 5.37024.7654 6.4668 6.1983 4.3450 5.3261輊犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏犏臌17編輯ppt()1,100,*,., 1, ., bbbXXXbB=*11000,.,XX,*11n bn bi bniTXXn=nnTX=(),2*,1111,n bnBnbootnn rbrvXXXXBB=-=邋*1005.001,X=0.0489,bootv=與直接用嵌入式估計(jì)得到的結(jié)果比較：4.997,nX

8、=20.0484,s=0.221bootbootsev=20.22ses=18編輯ppt()11,.,.,nnnnFXXTg XX揶=()*11,.,.,nnnnFXXTg XX揶=( )()( )()11nOnOBFnnbootFTTv=VV19編輯pptnT20編輯ppt()()nnGtTt=PnTnG()()*,11Bnn bbGtI TtB=21編輯ppt( )( )*bootnFnnBiasTTT=-E*1,.,BXX( )(),1,*,.,n bbn bbTg Xg XX=*,11nnn rrTTB=( )*nbootnnBiasTTT=-*bX22編輯ppt4.997nX =bo

9、otsebootBias( )*FXE23編輯ppt()*212,nCTTaa-=2nTzseanT*,1,.,nn BTT()*1222,2,nCTTTTaa-=-24編輯pptLSAT (Y) 576635558578666580555661651605653575545572594GPA (Z)3.393.302.813.033.443.073.003.433.363.133.122.742.762.882.9625編輯ppt0.132bootse標(biāo)準(zhǔn)誤差趨向穩(wěn)定于()()()()( ) ()( )22,YzYzyzdF y zydF yzdF zmmqmm-=-蝌蝌()()()()22

10、0.776iiiiiiiYYZZYYZZq-=-邋$B50100200400800160032000.1410.1370.1330.132bootse26編輯ppt0.137bootse*1,.,Bqq$q$()0.7820.51, 1.00 se=()0.46, 0.96 27編輯ppt()1,.,nXXX=()1*,.,nbXXX=( )(),1,*,.,n bbn bbTg Xg XX=*,1,.,bXbB=,*,1,.,n bTbB=28編輯ppt( )TT F=( )( )()1, ,.,nnnTT FTT Fg XX=()11,.,.,nnnnFXXTg XX揶=()*11,.,.

11、,nnnnFXXTg XX揶=( )()( )()11nOnOBFnnbootFTTv=VV29編輯ppt( )()(): 0.21,20.86,1FF XNN=+()1100,.,XX=XnnTX=bootsebootBias30編輯ppt* ,11Bn bootn bbTTB=31編輯ppt()1,.,0,nXXUniformq( )( )1nngGqqqqq-驏驏=桫 桫( )()()()1max,.,nGXXqqq=Q =PPq()max1max,.,nXXXq=()( )()1nnniiXFqqqq=驏= 桫Pq32編輯ppt( )()1max,.,nnXXX=()()()()*11

12、max,.,max,.,nnXXXXqq=PP()( ) is in the bootstrap samplenX= P()( )1 is not in the bootstrap samplenX=- P111nn驏=-桫()*0.632qq=P33編輯ppt()1,.,nXXX=()1max,.,nXXq=*q非參數(shù)bootstrap復(fù)制的直方圖B=1000，最高峰為 ()()*0.656011 10.6513nnqq=-=P理論結(jié)果：()1nngqqqq-驏驏=桫 桫g1q=0.8772q=34編輯pptnF()0,1FUniform=nF35編輯pptnF( )TT F=( )nnTT

13、 F=1,.,nXXn36編輯ppt();fxq();f xqF的先驗(yàn)nFqq();f xq();f xq()11,.,.,nnnXXTg XX揶=()*11,.,.,nnnXXTg XX揶=37編輯ppt()1max,.,0.8722nXXq=()0,fUniformq;()1,.,0,nXXUniformq1q=()0,0.8722fUniform;nF*bX( )*maxbbXq=*q的分布為真正的分布()1nnggqqqq-驏驏=桫 桫38編輯ppt2*,1111Bnbootn bn rbrvTTBB=驏=-桫邋0. 根據(jù)數(shù)據(jù) 估計(jì) f 的參數(shù) ，得到 f 的估計(jì)1. 抽取樣本2. 計(jì)

14、算3. 重復(fù)步驟1和2 B次，得到4.();f xqq1,.,nXX()*1,.,;nXXf xq:()*1,.,nnTg XX=*,1,.,nn BTT39編輯ppt二者相同的是模擬的思想();f xqnF40編輯ppt41編輯ppt42編輯pptnF1,.,nXX43編輯ppt44編輯ppt()1,.,nXXX=, 1,.,iXin=()()111,., ,.,iiinXXXXX-+=()111,.,.,iiinXXXXXX-+=BOOTSTRAP MATLAB TOOLBOX中也有該功能45編輯ppt()()(),niiTg X-=1,.,in=()111ninijijnXXXXnn-=

15、-()1,.,nnTg XX=46編輯ppt(),1,.,iXin-=()()(),niiTg X-=1,.,in=()2()()()()1111,nnninijackniniiinvTTTTnn-=-=-=邋jackjacksev=47編輯pptnnTX=()1nininXXTn-=-()()()111111111nnnninininiiiinXXTTnXXnnnnn-=-=-邋()()22()11111njackninniinvTTXXnnn-=-=-=-( )( )22, niXXnss=VV()( )22221, 1niSXXSns=-=-E方差的無偏估計(jì)()2111nnnn XnXXnn=