Mathematical Sciences: Some Problems in Saddlepoint Approximations in Statistics

点击翻译按钮获取中文摘要

The goal of this project is to develop new saddlepoint theory and methods, branching into areas not attacked in any depth to date. In particular, attention will be directed toward the use of saddlepoint approximations in the analysis of sample survey data, to saddlepoint expansions for resampling problems, and to saddlepoint expansions for a general quadratic form to be used in constructing confidence regions for nonparametric function estimation. For many modern statistical techniques employing sophisticated and often complicated estimators, there is an important technical difficulty in assessing the accuracy and precision of statistical estimators. For example, complex surveys yield data which usually require complicated mathematical forms for estimators of the quantities of interest. Making a clear statement about the amount of variability inherent in the estimation process is hindered by the intractability of the exact distributions of these estimators. Close approximations may replace these distributions; this work will utilize saddlepoint theory to develop such satisfactory approximate distributions.