Efficient estimation in missing data and survey sampling problems

Abstract

The thesis consists of four research papers. The first paper deals with general theory for empirical likelihood under the standard setup. Instead of maximizing the empirical likelihood function, a functional-form approach is proposed to generalize the theory of empirical likelihood and to achieve computational efficiency. The second paper deals with an empirical likelihood approach for missing data. The proposed method uses a partial likelihood for the respondents and theories are developed for both a parametric response model and a nonparametric response model. Also, the proposed method is extended to two-phase sampling where the first-phase sample is obtained by complex survey sampling. The third paper deals with empirical likelihood in the survey sampling setup. In the proposed method, called the population empirical likelihood method, the empirical likelihood function is defined for the finite population and the sampling design is incorporated into one of the constraints in the optimization problem. The proposed method is quite useful when combining information from several independent surveys. The fourth paper proposes a novel application of the capture-recapture experiment to estimate the propensity score for nonignorable nonresponse. The proposed method can be used to reduce the selection bias associated with voluntary sampling.