Consider the following bootstrap procedure Using the nonparametric bootstrap, generate bootstrap samples, calculate the estimate b on these samples and then calculate T (b b) s(b), where s(b) is the standard error in the original data Let q 2 and q 1 2 denote the 2th and 1 2th quantiles of T , and define the bootstrap confidence interval C bs(b)q 2, bs(b)q 1 2 Show that C exactly equals the percentile interval

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Question: Consider the following bootstrap procedure. Using the nonparametric bootstrap, generate bootstrap samples, calculate the estimate b on these samples and then calculate T

Consider the following bootstrap procedure. Using the nonparametric bootstrap, generate bootstrap samples, calculate the estimate bµ¤ on these samples and then calculate T ¤

Æ (bµ¤

¡ bµ)/s(bµ), where s(bµ) is the standard error in the original data. Let q¤

®/2 and q¤

1¡®/2 denote the ®/2th and 1¡®/2th quantiles of T ¤, and define the bootstrap confidence interval C Æ

£bµÅs(bµ)q¤

®/2, bµÅs(bµ)q¤

1¡®/2

Show that C exactly equals the percentile interval.

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