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Biometrika 1999 86(2):235-247; doi:10.1093/biomet/86.2.235
© 1999 by Biometrika Trust
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An empirical adjustment to the likelihood ratio statistic

TA Severini

Department of Statistics, Northwestern University, Evanston, IL 60208-4070, USA E-mail: severini@nwu.edu

Consider a model parameterised by a scalar parameter of interest {psi} and a nuisance parameter {lambda}. Inference about {psi} 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.

Key Words: ABC interval; Conditional inference; Confidence limits; Directed likelihood-ratio.


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