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# sol9 - (Q D A i B(C&P98 E f Phgy(fQ F E 0 exP E 5 63 D...

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Unformatted text preview: ' % (Q D % A ) ' i B(C&P98 E @ ' ' ' f % Phgy(fQ F E 0 ) @ exP E 5 63 D A @ f 8 (da(B ' @ (& D ' A ' @ f 8 aay(&T 0 ) @ VP u @ @ ( ) @ ) P& b X E E u E E cW X f X D YW x8 YW D b 8 cW f b b u YW D bcW f8 E yW b DX b 8 s q p u D cW (rvD . To compute the X fE X xw8 YW X 8 s q YW a(rp so E E b X 8 s q tD cW f YW (rp E X @ @ @ I aP` YW (2) standard error: and E ) @ ) f @ I PihP&Qge F E b @ @ ) (Pd cW E D A ' 8 5 3 ) ' % P(CBVUTSR4(&Q0 F ) ' % (& (1) and . For the confidence interval, and . For the median, . Everyone will get a different bootstrap standard error. I get . The normal interval is . For the percentile interval I get . # ! \$" DCBVU8 A ' E ) I E P&H % (G F D A @ (CB(98 5 ) ' % 0 764(&21 3 Hence, E E b X b cW f YW (rp 63 X 8 s q 5 b f b u D YW x8 W D X f X D yW Sw8 cW An 80 per cent confidence interval is confidence interval is E @ @ I & E 5 R3 (3) cent confidence interval In this case we get and the estimated standard error is Homework 9 Solutions . From the bootstrap I get . E (4) We may represent the bootstrap distribution as: 1 . . A 95 per cent and a 95 per D aVrp 8 s q " f D a(rp 8 s q " # ! f b b u b ef b b u D b U8 ef b D (rvu b 8 s q p D b ef 6A aaaA X 8 (rvD RA aa A X (rp s q p u 8 s q b b ef b f D 6A aaaA X (rp 8 s q b where D 8 (rp s q D 6A aaA X a(rp 8 s q DX 8 where . Now D 8 so D 6A a aA X 8 . . . D 6A aaaA X 8 . . . X X X D 8 b X and D 8 rD 6A aaA X 8 D 8 and D ef y b D f 8 8 D 6A aaA X a(rp 8 s q b D f 8 . Hence, Also, Treat the 's as fixed. Now 2 \$ HD 8 (rp s q ...
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