Empirical best prediction and hierarchical Bayes methods in small -area estimation

Model-based small-area estimation methods have received considerable importance over the last two decades. This dissertation investigates two popular methods, empirical best prediction (EBP) and hierarchical Bayes (HB) methods. These methods use appropriate mixed models in combining survey data and various census and administrative data. For the EBP approach, the dissertation considers the well-known Fay-Herriot (FH) model to demonstrate how both EBP and its measure of uncertainty can be improved. Practitioners like to use a method of moments (MOM) to estimate the model variance, but it often produces a negative estimate. In this case, a standard solution is to truncate the estimate at zero. This could, however, lead to significant loss of efficiency of EBP since the EBP reduces to a synthetic regression estimate which does not use survey information. A positive truncation point is suggested. Such a simple adjustment improves on small-sample properties of EBP in the Monte Carlo (MC) simulations and provides reasonable results in the data analysis on Small Area Income and Poverty data. A new weighted jackknife (WJ) estimator of the mean squared error (MSE) of EBP is proposed and a simple approximation to this estimator is provided. The WJ estimator is very accurate in the sense that its bias is of the order o(m−1). A MC simulation demonstrates that when m is small the WJ estimator performs better than both the un-weighted jackknife and the Taylor series MSE estimator. For the HB approach, a MC simulation is undertaken for a simple case of the FH model in order to study the frequentist\u27s properties of several possible prior distributions of the hyper-parameters. It turns out that the usual choice of uniform improper prior on the hyper-parameters does not provide good frequentist\u27s properties. However, the simulation results identify to a prior which provides good frequentist\u27s properties. Necessary and sufficient conditions on the prior distributions which yields proper posterior distributions are provided. A HB method is developed to estimate finite population proportions and is applied to estimate drug prevalence for different counties of Nebraska. Sufficient conditions are given in order to ensure the propriety of posterior distributions