Bootstrap estimation of actual significance levels for tests based on estimated nuisance parameters

Qiwei Yao, Wengyan Yang and Howell Tong

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Often for a non-regular parametric hypothesis, a tractable test statistic involves a nuisance parameter. A common practice is to replace the unknown nuisance parameter by its estimator. The validality of such a replacement can only be justified for an infinite sample in the sense that under appropriate conditions the asymptotic distribution of the statistic under the null hypothesis is unchanged when the nuisance parameter is replaced by its estimator (Crowder M.J. 1990. Biometrika 77: 499–506). We propose a bootstrap method to calibrate the error incurred in the significance level, for finite samples, due to the replacement. Further, we have proved that the bootstrap method provides a more accurate estimator for the unknown actual significance level than the nominal level. Simulations demonstrate the proposed methodology.

Keywords: bootstrap estimation; extreme value; hypothesis test; non-regular parametric family; nuisance parameter; significance level (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2001-11
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Published in Statistics and Computing, November, 2001, 11(4), pp. 367-371. ISSN: 0960-3174

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