Empirical and Hierarchical Bayes Methods in Small Area Estimation Problems

在大规模抽样调查中，经常对大量人口给出各种特征的估计。还需要对较小的领域或地区进行类似的估计。最近，人们相当重视改进与小面积估计问题有关的程序。传统的抽样调查估计方法使用的信息来自一个给定的小区域，由于该区域的样本量小，通常会产生较大的标准误差。许多联邦机构需要可靠的小地区统计数据来进行区域规划和分配政府资源。其中包括劳工统计局（Bureau of Labor Statistics）和人口普查局（Census Bureau）。前者不仅对全国的失业率，而且对各州的失业率都有兴趣；后者不可避免地漏掉了人口，必须面对在空间上对未被统计的人进行调整的问题。上一学年，他作为美国统计协会/国家科学基金会奖学金项目的高级研究员在劳工统计局和人口普查局工作。拟议的研究是他在这些机构旨在发展可靠的小地区统计数据的工作的继续。重点关注各种多元和时间序列模型，以结合相关来源的信息。计划是开发不同的经验和层次贝叶斯程序。为了确定经验贝叶斯估计量的精度，将寻求估计量的均方误差的二阶近似。这将需要将现有的方法扩展到多变量和时间序列模型，并扩展到用最大似然或有限最大似然方法估计先前参数的情况。预计后验均值和后验方差在层次贝叶斯分析中将涉及多维积分。我们将研究不同的基于抽样的积分计算方法。在这种情况下，将考虑吉布斯抽样方法的修正和近似。首席研究员在小区域估计方面有扎实的研究记录，并且经验丰富，与该领域的主要统计学家有合作关系，可以进行拟议的研究。他在这个项目中的成功将很容易在他熟悉的政府特定领域和其他重要领域得到应用。

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.