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Dr. Hackney STA Solutions pg 161

# Dr. Hackney STA Solutions pg 161 - For example if the...

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10-4 Solutions Manual for Statistical Inference 10 . 13 Here are the 35 distinct samples from { 2 , 4 , 9 , 12 } and their weights. { 12 , 12 , 12 , 12 } , 1 / 256 { 9 , 12 , 12 , 12 } , 1 / 64 { 9 , 9 , 12 , 12 } , 3 / 128 { 9 , 9 , 9 , 12 } , 1 / 64 { 9 , 9 , 9 , 9 } , 1 / 256 { 4 , 12 , 12 , 12 } , 1 / 64 { 4 , 9 , 12 , 12 } , 3 / 64 { 4 , 9 , 9 , 12 } , 3 / 64 { 4 , 9 , 9 , 9 } , 1 / 64 { 4 , 4 , 12 , 12 } , 3 / 128 { 4 , 4 , 9 , 12 } , 3 / 64 { 4 , 4 , 9 , 9 } , 3 / 128 { 4 , 4 , 4 , 12 } , 1 / 64 { 4 , 4 , 4 , 9 } , 1 / 64 { 4 , 4 , 4 , 4 } , 1 / 256 { 2 , 12 , 12 , 12 } , 1 / 64 { 2 , 9 , 12 , 12 } , 3 / 64 { 2 , 9 , 9 , 12 } , 3 / 64 { 2 , 9 , 9 , 9 } , 1 / 64 { 2 , 4 , 12 , 12 } , 3 / 64 { 2 , 4 , 9 , 12 } , 3 / 32 { 2 , 4 , 9 , 9 } , 3 / 64 { 2 , 4 , 4 , 12 } , 3 / 64 { 2 , 4 , 4 , 9 } , 3 / 64 { 2 , 4 , 4 , 4 } , 1 / 64 { 2 , 2 , 12 , 12 } , 3 / 128 { 2 , 2 , 9 , 12 } , 3 / 64 { 2 , 2 , 9 , 9 } , 3 / 128 { 2 , 2 , 4 , 12 } , 3 / 64 { 2 , 2 , 4 , 9 } , 3 / 64 { 2 , 2 , 4 , 4 } , 3 / 128 { 2 , 2 , 2 , 12 } , 1 / 64 { 2 , 2 , 2 , 9 } , 1 / 64 { 2 , 2 , 2 , 4 } , 1 / 64 { 2 , 2 , 2 , 2 } , 1 / 256 The verifications of parts ( a ) - ( d ) can be done with this table, or the table of means in Example A. 0 . 1 can be used. For part ( e ),verifying the bootstrap identities can involve much painful algebra, but it can be made easier if we understand what the bootstrap sample space (the space of all n n bootstrap samples) looks like. Given a sample x 1 , x 2 , . . . , x n , the bootstrap sample space can be thought of as a data array with n n rows (one for each bootstrap sample) and n columns, so each row of the data array is one bootstrap sample.
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Unformatted text preview: For example, if the sample size is n = 3, the bootstrap sample space is x 1 x 1 x 1 x 1 x 1 x 2 x 1 x 1 x 3 x 1 x 2 x 1 x 1 x 2 x 2 x 1 x 2 x 3 x 1 x 3 x 1 x 1 x 3 x 2 x 1 x 3 x 3 x 2 x 1 x 1 x 2 x 1 x 2 x 2 x 1 x 3 x 2 x 2 x 1 x 2 x 2 x 2 x 2 x 2 x 3 x 2 x 3 x 1 x 2 x 3 x 2 x 2 x 3 x 3 x 3 x 1 x 1 x 3 x 1 x 2 x 3 x 1 x 3 x 3 x 2 x 1 x 3 x 2 x 2 x 3 x 2 x 3 x 3 x 3 x 1 x 3 x 3 x 2 x 3 x 3 x 3 Note the pattern. The ﬁrst column is 9 x 1 s followed by 9 x 2 s followed by 9 x 3 s, the second column is 3 x 1 s followed by 3 x 2 s followed by 3 x 3 s, then repeated, etc. In general, for the entire bootstrap sample,...
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