Conditional limit laws for goodness-of-fit tests
Statistics Theory
2012-07-26 v1 Statistics Theory
Abstract
We study the conditional distribution of goodness of fit statistics of the Cram\'{e}r--von Mises type given the complete sufficient statistics in testing for exponential family models. We show that this distribution is close, in large samples, to that given by parametric bootstrapping, namely, the unconditional distribution of the statistic under the value of the parameter given by the maximum likelihood estimate. As part of the proof, we give uniform Edgeworth expansions of Rao--Blackwell estimates in these models.
Keywords
Cite
@article{arxiv.1207.5967,
title = {Conditional limit laws for goodness-of-fit tests},
author = {Richard A. Lockhart},
journal= {arXiv preprint arXiv:1207.5967},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.3150/11-BEJ366 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)