Conditional limit laws for goodness-of-fit tests

We study the conditional distribution of goodness of fit statistics of the Cramér-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 uncond...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2012-08, Vol.18 (3), p.857-882
Main Author: LOCKHART, RICHARD A.
Format: Article
Language:English
Subjects:
Approximation
Data sampling
Density
Distribution functions
empirical distribution function
goodness-of-fit
local central limit theorem
Maximum likelihood estimation
Maximum likelihood estimators
Null hypothesis
P values
parametric bootstrap
Rao–Blackwell
Sampling distributions
Statistics
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Summary:We study the conditional distribution of goodness of fit statistics of the Cramér-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.
ISSN:1350-7265
DOI:10.3150/11-BEJ366