Empirical Bayes methods in survey sampling

This dissertation concerns two problems in survey sampling: (a) small-area estimation and (b) estimation in finite population sampling. Both the topics have received considerable attention in recent years. Empirical Bayes method has been found to be very useful in small area estimator and finite population sampling. The method is very effective in combining relevant information from the sample surveys, various administrative records and the census data. The first half of the dissertation is devoted to small area estimation. In large scale national sample surveys, the sampling designs are determined so as to obtain reliable estimates of various characteristics of interest at the national level. Due to the availability of relatively small samples, the regular designed-based estimators perform poorly at the subnational level (e.g., state, county, etc.) when compared to the corresponding estimator at the national level. Similar situations arise when estimates are needed for a subgroup of the population obtained by classifying the population according to various demographic characteristics (e.g., age, race, sex, etc.). Such problems in survey sampling literature are known as small area estimation problems. Reliable small area statistics are needed in regional planning and in allocation of government resources. The following research has been conducted in the small area estimation problems: (a) A unified model is proposed which covers various specific small area models considered in the literature; (b) A general measure of uncertainty of the proposed empirical Bayes estimator is considered and (c) Small area estimation method under a random sampling variance model is developed. The later part of the dissertation concerns empirical Bayes estimation of different stratum means and variances when samples are obtained using a stratified simple random sampling design. The method is effective especially when moderately large samples are available from any given stratum. There are three main features of this research: (a) In order to reduce the effect of overshrinking bias associated with the usual empirical Bayes procedures, stratum specific random effects are introduced through the sampling variances; (b) General measures of uncertainty are proposed for the empirical Bayes point estimators of finite population means and variances; (c) Laplace\u27s second order approximation is used to approximate the one-dimensional integrals involved in the empirical Bayes point estimators and the measures of uncertainty of the point estimators. The approximation is especially helpful in obtaining the measures of uncertainty of the empirical Bayes estimators since the measures are based on Monte Carlo methods where checking the accuracy of the numerical integration method at each step of the replication is troublesome