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.
Original language | English (US) |
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Pages (from-to) | 235-247 |
Number of pages | 13 |
Journal | Biometrika |
Volume | 86 |
Issue number | 2 |
DOIs | |
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