Empirical and Hierarchical Bayes Methods in Small Area Estimation Problems

小区域估计问题中的经验和分层贝叶斯方法

• 批准号: 9206326
• 负责人: Parthasarathi Lahiri
• 金额: $ 5.5万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9206326&HistoricalAwards=false
• 关键词: Empirical; Hierarchical; Bayes; Methods; Small

In large scale sample surveys, estimates of a variety of characteristics are frequently given for large populations. Similar estimates for smaller domains or areas also are required. Recently, considerable attention has been given to improve procedures related to small area estimation problems. The traditional sample survey estimators which use information from a given small area often yield large standard errors because of small sample size in the area. Reliable small area statistics are needed by many federal agencies for regional planning and allocating government resources. Among these are the Bureau of Labor Statistics, which is interested in providing estimates of the unemployment rate not only for the nation but also for the states and the Census Bureau which inevitably misses people and must face the problem of adjusting spatially for the undercounts. The investigator spent the last academic year at the Bureau of Labor Statistics and the Census Bureau as a Senior Research Fellow under the American Statistical Association/ National Science Foundation Fellowship Program. The proposed research is a continuation of his work at these agencies aimed at developing reliable small area statistics. Attention is focussed on various multivariate and time series models to combine information from related sources. The plan is to develop different empirical and hierarchical Bayes procedures. To determine measures of accuracy of the empirical Bayes estimators, second order approximations will be sought to the mean squared errors of the estimators. This will require the extension of the existing methodology to multivariate and time series modelling and also to the situation when the prior parameters are estimated by the method of maximum likelihood or restricted maximum likelihood. It is anticipated that the posterior mean and the posterior variance in a hierarchical Bayes analysis will involve multi-dimensional integrals. Different sampling-based methods to evaluate the integrals will be investigated. In this context the modification and approximation of the Gibbs sampling method will be considered. The principal investigator has a solid research record in small area estimation and is well equipped by experience and by his collaborative ties with leading statisticians in the field to conduct the proposed research. His successes in this project will readily find applications in the particular areas of government with which he is familiar and other important arenas as well.

在大规模抽样调查中，经常给出对大量人口的各种特征的估计。对于较小的域或区域也需要类似的估计。最近，关于小面积估计问题的改进方法受到了相当大的关注。传统的抽样调查估计器使用的是给定小区域的信息，由于该区域的样本量较小，往往会产生较大的标准误差。许多联邦机构需要可靠的小区域统计数据来进行地区规划和分配政府资源。其中包括劳工统计局和人口普查局，前者不仅为全国，而且也为各州提供失业率估计，而人口普查局不可避免地遗漏了人口，必须面对因人口不足而在空间上进行调整的问题。这位调查员上一学年在劳工统计局和人口普查局担任美国统计协会/国家科学基金会奖学金计划下的高级研究员。这项拟议的研究是他在这些机构工作的继续，目的是开发可靠的小区域统计数据。注意力集中在各种多变量和时间序列模型上，以结合相关来源的信息。该计划是开发不同的经验和分级贝叶斯程序。为了确定经验贝叶斯估计量的精度，将寻求对估计量的均方误差的二阶近似。这将需要将现有方法扩展到多变量和时间序列建模，以及用最大似然法或限制最大似然法估计先验参数的情况。预计分层贝叶斯分析中的后验均值和后验方差将涉及多维积分。将研究不同的基于抽样的方法来评估积分。在这方面，将考虑Gibbs抽样方法的修改和近似。首席调查员在小区域估计方面拥有坚实的研究记录，并凭借经验和与该领域主要统计学家的合作关系，充分配备了进行拟议研究的能力。他在这个项目中的成功将很容易在他熟悉的特定政府领域以及其他重要领域得到应用。