Double Bootstrap

Double Bootstrap - Double Bootstrap Improve Accuracy of...

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Unformatted text preview: Double Bootstrap Improve Accuracy of Bootstrap Coverage Doug Steigerwald UC Santa Barbara January 2010 Sample Design Observe: random sample X = ( x 1 , . . . , x n ) Estimate μ via ˆ μ (may also have ˆ σ 2 ) Question: & How do we obtain a 95% con&dence interval with good coverage (and short distance)? coverage - probability that interval does contain true parameter value & For many problems, 95% con&dence interval has coverage of far less than 95% Single Bootstrap Initial Step random sample, with replacement, from ( x 1 , . . . , x n ) , generates & X ¡ = ( x ¡ 1 , . . . , x ¡ n ) & ˆ μ ¡ , ˆ σ ¡ 2 , t ¡ = ˆ μ ¡ ¢ ˆ μ ˆ σ ¡ construct R (single) bootstrap samples and order outcomes & n ˆ μ ¡ ( r ) o R r = 1 n t ¡ ( r ) o R r = 1 Con&dence Intervals R=999 Percentile CI: P & ˆ μ & ( 25 ) ¡ μ ¡ ˆ μ & ( 975 ) ¡ = . 95 & ˆ μ & ( 25 ) , ˆ μ & ( 975 ) ¡ Basic CI: P & ( ˆ μ & ¢ ˆ μ ) ( 25 ) ¡ ˆ μ ¢ μ ¡ ( ˆ μ & ¢ ˆ μ ) ( 975 ) ¡ = . 95 & ˆ...
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Double Bootstrap - Double Bootstrap Improve Accuracy of...

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