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.
Small area estimation is gaining increasing importance for policy makers both in the public and private sectors. As an example, the goal may be to obtain reliable estimates for counties, subcounties, census tracts etc. using data which were collected to achieve desired precision at a higher level of geography, for example at the state or the national level. Typically resources are unavailable to conduct a new survey to obtain estimates of required precision at the lower level of geography. Thus it becomes mandatory to combine data from several sources which include both survey data and administrative data. We have derived new small area estimation methods in order to address adequately problems of the above type. This includes estimation of median income at different levels of geography, states, counties etc., estimation of the number or proportion of children in the K-12 grades under poverty, disbursement of money for education and others. The new techniques that are developed rectify some of the limitations of methods that were prescribed earlier. The new statistical methods that are developed go well beyond the scope of small area estimation. The model-based estimates that are produced can be applied to other social and economic data, not necessarily restricted to small areas. A potential useful application is in the area of animal science.
