How close are alternative bootstrap P-values?

Chris J. Lloyd

Statistics & Probability Letters, 2010, vol. 80, issue 23-24, 1972-1976

Abstract: The parametric bootstrap P-value based on a test statistic T is the exact tail probability of the observed value t, with the null maximum likelihood estimate of the nuisance parameters substituted. This P-value is known to lead to tests whose size is closer to nominal asymptotically than the first order test. One issue that has not been addressed is whether parametric bootstrap might reduce the impact of the choice of basic test statistic. It is shown that bootstrap P-values based on different first order statistics differ to second order i.e to O(m-1) where m is a measure of sample size. Boostrap reduces the impact of the test statistic choice. Just as importantly, it is shown numerically that this asymptotic rate may under-estimate how close alternative bootstrap P-values are for small sample sizes.

Keywords: Nuisance; parameters; Second; order; asymptotics; Bootstrap (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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