Mathematical Sciences: Some Problems in Saddlepoint Approximations in Statistics

这个项目的目标是开发新的鞍点 理论和方法，分支到领域没有攻击任何 深度到目前为止。 特别是，注意力将集中在 鞍点近似在样品分析中的应用 调查数据，到重采样问题的鞍点展开， 和鞍点展开的一般二次型是 用于构建非参数的置信区域 函数估计 对于许多现代统计技术， 复杂的，往往是复杂的估计，有一个 评估准确性的重要技术困难， 统计估计的精度。例如，复杂的调查 产生通常需要复杂数学形式的数据 对于感兴趣的量的估计器。 作出明确 关于变量固有量的声明 估计过程受到精确的难以处理的阻碍。 这些估计量的分布。 近似值可以 替换这些分布;这项工作将利用鞍点 理论来开发这种令人满意的近似分布。

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.