Bernoulli

  • Bernoulli
  • Volume 2, Number 2 (1996), 145-165.

An explicit large-deviation approximation to one-parameter tests

Ib M. Skovgaard

Full-text: Open access

Abstract

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*.

Article information

Source
Bernoulli Volume 2, Number 2 (1996), 145-165.

Dates
First available in Project Euclid: 31 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1193839221

Digital Object Identifier
doi:10.3150/bj/1193839221

Mathematical Reviews number (MathSciNet)
MR1410135

Zentralblatt MATH identifier
1066.62508

Keywords
conditional inference large-deviation expansions modified log-likelihood ratio test nuisance parameters parametric inference

Citation

Skovgaard, Ib M. An explicit large-deviation approximation to one-parameter tests. Bernoulli 2 (1996), no. 2, 145--165. doi:10.3150/bj/1193839221. https://projecteuclid.org/euclid.bj/1193839221


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