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June 1996 An explicit large-deviation approximation to one-parameter tests
Ib M. Skovgaard
Bernoulli 2(2): 145-165 (June 1996). DOI: 10.3150/bj/1193839221


An approximation is derived for tests of one-dimensional hypotheses in a general regular parametric model, possibly with nuisance parameters. The test statistic is most conveniently represented as a modified log-likelihood ratio statistic, just as the R*-statistic from Barndorff-Nielsen (1986). In fact, the statistic is identical to a version of R*, except that a certain approximation is used for the sample space derivatives required for the calculation of R*. With this approximation the relative error for large-deviation tail probabilities still tends uniformly to zero for curved exponential models. The rate may, however, be O(n-1/2) rather than O(n-1) as for R*. For general regular models asymptotic properties are less clear but still good compared to other general methods. The expression for the statistic is quite explicit, involving only likelihood quantities of a complexity comparable to an information matrix. A numerical example confirms the highly accurate tail probabilities. A sketch of the proof is given. This includes large parts which, despite technical differences, may be considered an overview of Barndorff-Nielsen's derivation of the formulae for p* and R*.


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Ib M. Skovgaard. "An explicit large-deviation approximation to one-parameter tests." Bernoulli 2 (2) 145 - 165, June 1996.


Published: June 1996
First available in Project Euclid: 31 October 2007

zbMATH: 1066.62508
MathSciNet: MR1410135
Digital Object Identifier: 10.3150/bj/1193839221

Keywords: conditional inference , large-deviation expansions , modified log-likelihood ratio test , nuisance parameters , Parametric inference

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability

Vol.2 • No. 2 • June 1996
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