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

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