Bayesian Empirical Likelihood and Penalized Splines for Small Area Estimation

这项研究将发展新的基于经验似然和惩罚样条法的小区域估计的半参数贝叶斯方法。该方法也适用于某些随机和固定效应模型。这些方法将允许在处理问题时有更大的灵活性，在这些问题中，可能性正态假设、线性假设或两者都可能受到质疑。经验似然没有任何似然的参数结构，而惩罚样条法可以避免假定响应和协变量之间存在特定的函数关系。随机效应的Dirichlet过程混合先验的引入克服了随机效应的高斯性这一不可验证的、有时是值得怀疑的假设。此外，当出于管理目的需要对小区域进行集群时，这些优先级尤其有用。该研究将通过仿真研究来检验新方法的稳健性。惩罚样条法与经验似然法的集成也将被研究。小面积估计对于美国的每个联邦机构都是至关重要的。例如，美国人口普查局的小区域收入和贫困估计(SAIPE)项目，劳工统计局所需的当地失业率，美国农业部的小区域农业现金租金计划，以及学区级K-12年级贫困儿童的估计，这些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，在帮助当地企业决策方面。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、县以下县和人口普查区域。在这方面，各种问题的性质和相关的复杂性要求不断改进现有方法和开发新技术。因此，新的小区域估计方法的发展为实际应用带来了巨大的希望。作为支持调查和统计方法研究的联合活动的一部分，该项目得到了方法学、测量和统计方案和一个联邦统计机构联盟的支持。

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.