A modified likelihood ratio statistic for some nonregular models

Thomas A. Severini

doi:10.1093/biomet/91.3.603

A modified likelihood ratio statistic for some nonregular models

Thomas A. Severini^*

^*Corresponding author for this work

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Higher-order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on 9. A modified likelihood ratio statistic is proposed that follows its asymptotic distribution to a high degree of approximation, and this statistic is illustrated on several examples.

Original language	English (US)
Pages (from-to)	603-612
Number of pages	10
Journal	Biometrika
Volume	91
Issue number	3
DOIs	https://doi.org/10.1093/biomet/91.3.603
State	Published - 2004

Funding

I would like to thank the associate editor for comments which have greatly improved the presentation. This work was supported by the U.S. National Science Foundation.

Keywords

Higher-order asymptotic theory
Likelihood ratio approximation
Maximum likelihood
Unknown endpoint

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics, Probability and Uncertainty
Applied Mathematics

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PY - 2004

Y1 - 2004

N2 - Higher-order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on 9. A modified likelihood ratio statistic is proposed that follows its asymptotic distribution to a high degree of approximation, and this statistic is illustrated on several examples.

AB - Higher-order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on 9. A modified likelihood ratio statistic is proposed that follows its asymptotic distribution to a high degree of approximation, and this statistic is illustrated on several examples.

KW - Higher-order asymptotic theory

KW - Likelihood ratio approximation

KW - Maximum likelihood

KW - Unknown endpoint

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ER -

A modified likelihood ratio statistic for some nonregular models

Abstract

Funding

Keywords

ASJC Scopus subject areas

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