An empirical adjustment to the likelihood ratio statistic

Thomas A. Severini

doi:10.1093/biomet/86.2.235

An empirical adjustment to the likelihood ratio statistic

Thomas A. Severini^*

^*Corresponding author for this work

Statistics and Data Science

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

36 Scopus citations

Abstract

Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n^-1/2). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this paper, an approximation to R* is proposed that can be calculated numerically for a wide range of models. This approximation is shown to agree with R* with error of order O_p(n^-1). The results are illustrated on several examples.

Original language	English (US)
Pages (from-to)	235-247
Number of pages	13
Journal	Biometrika
Volume	86
Issue number	2
DOIs	https://doi.org/10.1093/biomet/86.2.235
State	Published - 1999

Keywords

ABC interval
Conditional inference
Confidence limits
Directed likelihood-ratio

ASJC Scopus subject areas

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

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10.1093/biomet/86.2.235

Cite this

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title = "An empirical adjustment to the likelihood ratio statistic",

abstract = "Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n-1/2). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this paper, an approximation to R* is proposed that can be calculated numerically for a wide range of models. This approximation is shown to agree with R* with error of order Op(n-1). The results are illustrated on several examples.",

keywords = "ABC interval, Conditional inference, Confidence limits, Directed likelihood-ratio",

author = "Severini, {Thomas A.}",

note = "Funding Information: I would like to thank the associate editor for many useful comments and suggestions. This paper was presented at the Centre de Recherches Math{\'e}matiques Summer School on Likelihood and Asymptotics, held at Banff, Canada in August, 1997; I am grateful to the participants for their helpful comments. This work was supported by the National Science Foundation.",

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doi = "10.1093/biomet/86.2.235",

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journal = "Biometrika",

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AU - Severini, Thomas A.

N1 - Funding Information: I would like to thank the associate editor for many useful comments and suggestions. This paper was presented at the Centre de Recherches Mathématiques Summer School on Likelihood and Asymptotics, held at Banff, Canada in August, 1997; I am grateful to the participants for their helpful comments. This work was supported by the National Science Foundation.

PY - 1999

Y1 - 1999

N2 - Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n-1/2). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this paper, an approximation to R* is proposed that can be calculated numerically for a wide range of models. This approximation is shown to agree with R* with error of order Op(n-1). The results are illustrated on several examples.

AB - Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n-1/2). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this paper, an approximation to R* is proposed that can be calculated numerically for a wide range of models. This approximation is shown to agree with R* with error of order Op(n-1). The results are illustrated on several examples.

KW - ABC interval

KW - Conditional inference

KW - Confidence limits

KW - Directed likelihood-ratio

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SN - 0006-3444

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An empirical adjustment to the likelihood ratio statistic

Abstract

Keywords

ASJC Scopus subject areas

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