Mathematical Sciences: Some Estimation and Computation Procedures in Statistics

题目：统计学中的一些估计和计算程序摘要：本研究的主要目的是在抽样、缺失数据分析和测量误差模型等统计问题的一些重要类别中发展新的理论和方法。研究课题是由实际问题驱动的，主要集中在估计和（近似）计算过程。该研究旨在显著提高这些领域的统计知识，特别是改进调查机构的一些现行做法。在解决某些问题时，需要使用小样本渐近方法。研究了精确鞍点近似在这些问题中的潜在应用。在其他提出的问题中，研究了大样本渐近方法。研究课题包括数据部分缺失或测量误差时的回归核估计；抽样调查中的子域估计；对有限总体的分布函数进行了新的最优估计。在这个研究项目中，新的统计理论和方法得到发展，并在具有实际意义的统计问题上进行了研究。准确性和简洁性是开发此类统计方法的主要标准。它们直接应用于各种机构，如劳工统计局，以提高当前统计实践的准确性和速度。此外，这项研究还推动了高性能计算和生物技术统计方面的联邦战略领域的科学和技术。

Proposal: DMS 9504589 PI: Suojin Wang Institution: Texax A&M Title: SOME ESTIMATION AND COMPUTATION PROCEDURES IN STATISTICS Abstract: The primary objective of this research is to develop new theory and methods in some important classes of statistical problems in the areas of sampling, missing data analysis and measurement error models. The research topics are motivated by practical problems and the main focus is on estimation and (approximate) computation procedures. The research aims to significantly advance statistical knowledge in these areas, and improve some current practices in survey agencies in particular. In attacking some of the proposed problems, small sample asymptotic methods are desired. The potential use of accurate saddlepoint approximations in these problems is studied. In other proposed problems, large sample asymptotic methods are investigated. The research topics include kernel-type estimations in regression when data are partially missing or measured with error; sub-domain estimation in sample surveys; and new and optimal estimation of the distribution function of a finite population. In this research project new statistical theory and methods are developed and investigated in statistical problems that bear practical importance. The accuracy and simplicity are the main criteria in developing such statistical methods. They have direct applications in various agencies, such as the Bureau of Labor Statistics, to improve the accuracy and speed of the current statistical practice. Furthermore, this research advances the science and technology in the Federal Strategic Areas of high performance computing and the statistical aspects of biotechnology.