Institute of Mathematical Statistics Lecture Notes - Monograph Series

A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations

Juan Zhang and John E. Kolassa

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Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic $R$. The standard normal approximation to the conditional distribution of $R$ typically has error of order $O(n^{-1/2})$, where $n$ is the sample size. There are several modifications for $R$, which reduce the order of error in the approximations. In this paper, we mainly investigate Barndorff-Nielsen's modified directed likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and Martin's two modifications, involving the Bayesian approach and the conditional likelihood ratio statistic. For each modification, two formats were employed to approximate the conditional cumulative distribution function; these are Barndorff-Nielson formats and the Lugannani and Rice formats. All approximations were applied to inference on the ratio of means for two independent exponential random variables. We constructed one and two-sided hypotheses tests and used the actual sizes of the tests as the measurements of accuracy to compare those approximations.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 250-259

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Primary: 62E60 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

modified signed likelihood ratio statistic saddlepoint approximation conditional cumulative distribution

Copyright © 2007, Institute of Mathematical Statistics


Zhang, Juan; Kolassa, John E. A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations. Complex Datasets and Inverse Problems, 250--259, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000193.

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