Higher order conditional inference using parallels with approximate Bayesian techniques

Abstract

OF THE DISSERTATION Higher order conditional inference using parallels with approximate Bayesian techniques by JUAN ZHANG Dissertation Director: John E. Kolassa I consider parametric models with a scalar parameter of interest and multiple nuisance parameters. The likelihood ratio statistic is frequently used in statistical inference. The standard normal approximation to the likelihood ratio statistic generally has error of order O(n−1/2), where n denotes the sample size. When n is small, the normal approximation may not be adequate to do accurate inference. In practice, the true error is more important than asymptotic order. The intention of this study is to find an approximation which is relatively easy to apply, but which is accurate under small sample size settings. Saddlepoint approximations are well-known for higher order accuracy properties and remarkably good relative error properties. There are several saddlepoint approximations. I look for one that is flexible in application while keeping a satisfactory convergence rate. I evaluate, via Monte Carlo, the accuracies of several saddlepoint approximations, and of some classical methods, when these approximations are used to approximate p-values for hypotheses about a scalar parameter. Based on the results, I find that DiCiccio and Martin’s (1993) approximations are interesting