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

该研究项目将开发基于经典和贝叶斯模型的统计程序，其主要目标是为代表当地地理区域和/或人口亚组的小区域提供准确的估计。 这项研究的主要动机源于需要精确估计的小面积，这有利于联邦政府的能力，以启动，制定和最终实施各种社会经济方案，以解决，除其他外，各种公共卫生问题，收入和贫困在地方一级。 通常，大多数人口调查的目的是在全球一级实现高效率，这导致对较小地区的直接调查估计数具有较大的标准误差。 在许多调查中（例如，目前的人口调查和目前的就业统计调查），数据也收集了随着时间的推移提供有用的时间序列。 该项目将利用数据的时间序列性质，并通过借用小区域信息以及长期以来可获得的信息的力量，对小区域进行可靠的估计。 显式模型将开发纳入线性以及一些最近开发的非线性时间序列模型。 在这方面，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有用的各种联邦和地方政府的计划。 马尔可夫链蒙特卡罗方法将用于拟合贝叶斯模型。 将开发基于SAS、FORTRAN、S-plus和SCA的软件，用于实施本项目中开发的方法。 此外，小面积估计的准确性的措施将通过二阶近似这些估计的均方误差进行评估，即使当潜在的分布是未指定的，以检查最终结果是强大的对non-normalization.The重要性这个项目在于它的相关性和直接联系到一些正在进行的计划在人口普查局和劳工统计局。 这项研究将导致精确估计（i）贫困率和家庭收入中位数在小地区收入和贫困估计计划由人口普查局推出，（ii）美国平民失业率，（iii）准确就业计数各地区的主要行业。 这项研究一方面将推进小面积估计的统计方法，另一方面将把各种新开发的方法应用于对社会重要的统计问题。

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.