Bayesian Empirical Likelihood and Penalized Splines for Small Area Estimation

本研究将发展新的半参数贝氏方法，以经验似然与惩罚样条为基础，进行小区域的估计。 该方法也可以适用于某些随机和固定效应模型。 这些方法将允许在处理可能性、线性或两者的正态性假设可能受到质疑的问题时具有更大的灵活性。 经验似然函数不需要任何似然函数的参数结构，而惩罚样条函数可以避免假设响应和协变量之间存在特定的函数关系。 随机效应的狄利克雷过程混合先验的引入克服了随机效应的高斯性的不可验证的，有时是有疑问的假设。 此外，这些先验是特别有用的，当一个人需要集群的小区域的管理目的。 这项研究将通过模拟研究来检验新方法的稳健性。 惩罚样条与经验似然的集成也将被研究。小面积估计已经成为美国每个联邦机构的重要组成部分。 例子包括美国人口普查局的小地区收入和贫困估计（SAIPE）项目，劳工统计局需要的当地失业率，美国农业部的小地区农业现金租金计划，以及在学区一级对K-12年级贫困儿童的估计，这对教育部和许多其他项目都很有用。 小面积估算对私营部门也很重要;例如，有助于当地企业的决策。 所有这些的统一主题是，人们需要在较低的地理水平上进行可靠的估计，如县、县以下和人口普查区。 问题的性质各不相同，这方面的问题也很复杂，因此需要不断改进现有的方法和开发新的技术。 因此，新的小面积估计方法的发展具有很大的希望，为真实的生活应用。 该项目得到了方法、测量和统计方案以及联邦统计机构联合会的支持，作为支持调查和统计方法研究的联合活动的一部分。

This research will develop new semiparametric Bayesian methods for small area estimation based on empirical likelihood and penalized splines. The approach also can be adapted for certain random and fixed effects models. These methods will allow for greater flexibility in handling problems where assumptions of normality of the likelihood, the linearity, or both can be subject to question. Empirical likelihood dispenses with any parametric structure of the likelihood, while penalized splines can avoid the assumption of a specific functional relationship between the response and the covariates. The introduction of Dirichlet process mixture priors for random effects overcomes the unverifiable and sometimes questionable assumption of Gaussianity of random effects. Further, these priors are particularly helpful when one requires clustering of small areas for administrative purposes. The research will examine the robustness of the new methods through simulation studies. The integration of penalized splines with empirical likelihood also will be investigated.Small area estimation has become vital for every Federal agency in the United States. Examples include the Small Area Income and Poverty Estimation (SAIPE) project of the United States Bureau of the Census, local area unemployment rates as needed by the Bureau of Labor Statistics, small area agricultural cash rent program of the United States Department of Agriculture, and the estimation of children under poverty in K-12 grades at the school district level, which are useful for the Department of Education and many other projects. Small area estimation also is important for the private sector; for example, in aiding the decision making of local businesses. The unifying theme in all these is that one needs reliable estimates at lower levels of geography, such as counties, subcounties, and census tracts. The varied nature of problems and the associated complexity in this regard demands a continuous enhancement of existing methods and the development of new techniques. The development of new small area estimation methodology therefore holds great promise for real life applications. The project is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.