Parametric and Semiparametric Bayesian Methods for Small Area Estimation

本研究的重点是发展小面积估计的参数和半参数分层贝叶斯方法。 直接调查估计的局部地区（如县，市，或人口普查司）通常伴随着大的标准误差和变异系数，由于在这些地区的样本量小。 其主要原因是，最初的调查目标是在比地方地区高得多的总体水平上实现准确性。 因此，有必要“借势”或利用当地类似地区的信息。 分层和经验贝叶斯方法特别适合满足这一需求。 然而，大部分贝叶斯文献仅限于小区域均值和其他感兴趣特征的正态理论分层和经验贝叶斯估计，并且几乎完全是参数化的，假设局部区域效应的正态性。 本研究的主要组成部分之一是半参数分层贝叶斯方法，避免假设当地的影响正态的发展。 这些方法适用于线性和广义线性模型。 这些方法的具体应用将涉及估计四口之家的收入中位数，估计收入和贫困的小地方，如县，县，人口普查区等的方法适用于其他问题，并可用于离散和连续数据的分析。 本研究的第二个方面是小面积估计更复杂的调查，如分层两阶段抽样，其中的局部区域包括跨越地层边界的主要单位。 参数和半参数分层贝叶斯方法将在这里进行，并将结果进行比较。

This research focuses on the development of parametric and semiparametric hierarchical Bayesian methods for small area estimation. Direct survey estimates of local areas (such as a county, municipality, or census division) are usually accompanied by large standard errors and coefficients of variation due to smallness of samples sizes in these areas. The prime reason for this is that the original survey was targeted to achieve accuracy at a much higher level of aggregation than that for local areas. This makes it a necessity to `borrow strength` or use information from similar local areas. Hierarchical and empirical Bayes methods are particularly well-suited to meet this need. Much of the Bayesian literature, however, is restricted to normal theory hierarchical and empirical Bayes estimation of small area means and other characteristics of interest, and that too has almost exclusively been parametric, assuming normality of the local area effects. One of the major components of this research is the development of semiparametric hierarchical Bayesian methods that avoid assuming normality of the local area effects. These methods are applicable to both linear and generalized linear models. Specific applications of these methods will involve estimation of median income of four-person families, estimation of income and poverty for small places like counties, subcounties, census tracts, etc. The methodology is applicable to other problems and can be used for the analysis of both discrete and continuous data. The second aspect of this research is small area estimation for more complex surveys, such as stratified two-stage sampling, where the local areas consist of primary units which cut across the stratum boundaries. Both parametric and semiparametric hierarchical Bayesian methods will be pursued here and the results will be compared.