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.
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