Empirical likelihood for unit level models in small area estimation

Abstract

In this thesis we discuss semiparametric Bayesian empirical likelihood methods for unit level models in small area estimation. Our methods combine Bayesian analysis and empirical likelihood. In our method, we replace the parametric likelihood by an empirical likelihood which for a proposed value of the parameters estimates the data likelihood from a constrained empirical distribution function. No specific parametric form of the likelihood needs to be specified. The parameters influence the procedure through the constraints under which the likelihood is estimated.We focus on the empirical-likelihood-based methods for unit level small area estimation. Depending on the size of the actual data available, which may not be much, several models can be used. We discuss two such models here. The first is the separate unit level model which treats each area individually. If the number of observations in each area is too low, we use the joint unit level model. We discuss the suitability of the proposed likelihoods in Bayesian inference and illustrate their performances in two studies with real data sets.