Cross-Sectional and Time Series Approaches to Small Area Estimation: Methods and Applications

这一研究项目将制定经典的和基于贝叶斯模型的统计程序，主要目标是提供代表当地地理区域和(或)人口分组的小区域的准确估计。这项研究的主要动机是需要对小区域进行准确的估计，这有助于联邦政府启动、制定并最终实施各种社会经济计划，以解决各种公共卫生问题以及地方一级的收入和贫困问题。通常，大多数人口调查的目的是在全球一级实现高水平的效率，这导致对较小地区的直接调查估计具有较大的标准误差。在许多调查中(例如，当前的人口调查和当前的就业统计调查)，数据也是随着时间的推移而收集的，提供了有用的时间序列。该项目将利用数据的时间序列性质，通过借用小区域以及随着时间推移可用的信息的力量，对小区域作出可靠的估计。显式模型将结合线性和最近发展的一些非线性时间序列模型来开发。在此背景下，这项研究将开发合适的统计方法，如经验最佳线性无偏预测、经验贝叶斯和分层贝叶斯估计方法，以产生可靠的小面积点和区间估计，用于各种联邦和地方政府计划。马尔可夫链蒙特卡罗方法将用于贝叶斯模型的拟合。将开发基于SAS、FORTRAN、S+和SCA的软件来实施本项目中开发的方法。此外，小区域估计器的精确度将通过这些估计器的均方误差的二阶近似来评估，即使在基础分布未指定的情况下也是如此，以检查最终结果是否针对非正态分布是稳健的。这个项目的重要性在于它与人口普查局和劳工统计局正在进行的一些计划的相关性和直接联系。这项研究将导致对(I)人口普查局发起的小地区收入和贫困估计计划中的贫困率和家庭收入中位数的准确估计，(Ii)美国平民失业率的准确估计，以及(Iii)各地区主要行业的准确就业统计。这项研究一方面将推进小面积估计的统计方法，另一方面将各种新开发的方法应用于对社会具有重要意义的统计问题。

This research project will develop classical and Bayesian model-based statistical procedures with the primary goal of providing accurate estimates for small areas, representing local geographical regions and/or demographic subgroups of population. Primary motivation for this research stems from the need for precise estimates of small areas which facilitates the federal government's ability to initiate, formulate, and finally implement various socio-economic programs in order to address, among others, various public health issues, and income and poverty at local levels. Usually, most population surveys are designed to achieve a high level of efficiency at the global level which leads to direct survey based estimates of smaller areas having large standard errors. In many surveys (e.g., the Current Population Survey and the Current Employment Statistics Survey), data also are collected over time providing useful time series. This project will exploit the time series nature of data and produce reliable estimates of small areas by borrowing strength from information across small areas as well as those available over time. Explicit models will be developed incorporating linear as well as some recently developed nonlinear time series models. In this context, the study will develop suitable statistical methodologies such as empirical best linear unbiased prediction, empirical Bayes and hierarchical Bayes estimation methods to produce reliable small area point and interval estimates useful in various federal and local government programs. Markov chain Monte Carlo methods will be used in fitting Bayesian models. Software based on SAS, FORTRAN, S-plus, and SCA will be developed for implementing methodologies developed in this project. Furthermore, measure of accuracy of small area estimators will be assessed through second order approximations for the mean squared error of these estimators, even when the underlying distributions are unspecified, to check if the end results are robust against non-normality.The importance of this project lies in its relevance and direct tie to some of the on-going programs in the Census Bureau and the Bureau of Labor Statistics. This research will lead to precise estimates of (i) poverty rates and median family income in the Small Area Income and Poverty Estimates program launched by the Census Bureau, (ii) U.S. civilian unemployment rates, and (iii) accurate employment counts for major industries in various regions. This research will, on the one hand, advance statistical methodology for small area estimation and, on the other hand, apply various newly developed methodologies to statistical issues important to society.