Yao, Q. and Zhang, W. and Tong, H. (2001) Bootstrap estimation of actual significance levels for tests basedon estimated nuisance parameters. Statistics and Computing, 11 (4). pp. 367-371. ISSN 0960-3174 .
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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.
|Uncontrolled keywords:||bootstrap estimation; extreme value; hypothesis test; non-regular parametric family; nuisance parameter; significance level|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics|
|Depositing User:||Judith Broom|
|Date Deposited:||11 Oct 2008 22:09|
|Last Modified:||14 Jan 2010 14:41|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/10601 (The current URI for this page, for reference purposes)|
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