统计学bootstrap

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

2、骣=-换桫PiX9编辑ppt()( ),11BPnn bnnbTTtdGtTB=EnT,1,.,nn BTTnT( )nTEnT( )nTEnGnGB10编辑ppt()()()( )(),11BPn bnnbh Th t dGth TB=E()()()( )22,11BPn bnnnnbTTTTTB=-=EV( )nTV()()2,n bn bnh TTT=-B11编辑ppt1*,.,nXX()1*,.,nnTg XX=1*,.,nnXXFnTnFnFnFnF1,.,nXX12编辑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编辑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编辑ppt()()22,TTnt

4、dGtsm=-( )2FnTTns=V()TntdGtm=( )()2*,1111, nBBnn bnnn bFbbTTTTTBB=-=邋V( )FnTV( )nnFTV( )nnFTVnF15编辑ppt（大数定律）2*,1111Bnbootn bn rbrvTTBB=骣=-桫邋（计算boostrap样本）（计算boostrap复制）*1,.,nnXXF:()*1,.,nnTg XX=*,1,.,nn BTT16编辑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、计结果：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轾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编辑ppt()1,100,*,., 1, ., bbbXXXbB=*11000,.,XX,*11n bn bi bniTXXn=nnTX=(),2*,1111,n bnBnbootnn rbrvXXXXBB=-=邋*1005.001,X=0.0489,bootv=与直接用嵌入式估计得到的结果比较：4.997,nX

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

9、otsebootBias( )*FXE23编辑ppt()*212,nCTTaa-=2nTzseanT*,1,.,nn BTT()*1222,2,nCTTTTaa-=-24编辑pptLSAT (Y) 576635558578666580555661651605653575545572594GPA (Z)3.393.302.813.033.443.073.003.433.363.133.122.742.762.882.9625编辑ppt0.132bootse标准误差趋向稳定于()()()()( ) ()( )22,YzYzyzdF y zydF yzdF zmmqmm-=-蝌蝌()()()()22

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

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

12、max,.,max,.,nnXXXXqq=PP()( ) is in the bootstrap samplenX= P()( )1 is not in the bootstrap samplenX=- P111nn骣=-桫()*0.632qq=P33编辑ppt()1,.,nXXX=()1max,.,nXXq=*q非参数bootstrap复制的直方图B=1000，最高峰为 ()()*0.656011 10.6513nnqq=-=P理论结果：()1nngqqqq-骣骣=桫 桫g1q=0.8772q=34编辑pptnF()0,1FUniform=nF35编辑pptnF( )TT F=( )nnTT

13、 F=1,.,nXXn36编辑ppt();fxq();f xqF的先验nFqq();f xq();f xq()11,.,.,nnnXXTg XX揶=()*11,.,.,nnnXXTg XX揶=37编辑ppt()1max,.,0.8722nXXq=()0,fUniformq;()1,.,0,nXXUniformq1q=()0,0.8722fUniform;nF*bX( )*maxbbXq=*q的分布为真正的分布()1nnggqqqq-骣骣=桫 桫38编辑ppt2*,1111Bnbootn bn rbrvTTBB=骣=-桫邋0. 根据数据 估计 f 的参数 ，得到 f 的估计1. 抽取样本2. 计

14、算3. 重复步骤1和2 B次，得到4.();f xqq1,.,nXX()*1,.,;nXXf xq:()*1,.,nnTg XX=*,1,.,nn BTT39编辑ppt二者相同的是模拟的思想();f xqnF40编辑ppt41编辑ppt42编辑pptnF1,.,nXX43编辑ppt44编辑ppt()1,.,nXXX=, 1,.,iXin=()()111,., ,.,iiinXXXXX-+=()111,.,.,iiinXXXXXX-+=BOOTSTRAP MATLAB TOOLBOX中也有该功能45编辑ppt()()(),niiTg X-=1,.,in=()111ninijijnXXXXnn-=

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