Biometrika Advance Access originally published online on June 9, 2008
Biometrika 2008 95(3):747-758; doi:10.1093/biomet/asn011
Articles |
Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families
Department of Social Statistics, Cornell University, Ithaca, New York 14853, U.S.A. tjd9{at}cornell.edu
Department of Mathematics, Imperial College London, London, SW7 2AZ, U.K. alastair.young{at}imperial.ac.uk
Received for publication 1 November 2006. Revision received 1 October 2007.
Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional properties in providing third-order relative accuracy in approximation of p-values associated with the optimal test, in both continuous and discrete models. The bootstrap approach is equivalent to third-order analytical approaches, and is demonstrated in a number of examples to give very accurate approximations even for very small sample sizes.
Key Words: Bootstrap • Conditional test • Full exponential family • Likelihood • Nuisance parameter • Signed root likelihood ratio statistic
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