Empirical and hierarchical bayesian methods with applications to small area estimation

The topic of this dissertation focuses on the formulation of empirical and hierarchical Bayesian techniques in the context of small area estimation.;In the first part of the dissertation, we consider robust Bayes and empirical Bayes (EB) procedure for estimation of small area means. We have introduced the notion of influence functions in the small area context, and have developed robust Bayes and EB estimators based on such influence functions. We have derived an expression for the predictive influence function, and based on a standardized version of the same, we have proposed some new small area estimators. The mean squared errors and estimated mean squared errors of these estimators have also been found. The findings are validated by a simulation study.;In the second part, we have considered small area estimation for bivariate binary data in the presence of covariates. We have developed EB estimators along with their mean squared errors. In this case the covariates were assumed to be completely observed. In the presence of missing covariates, we have developed a hierarchical Bayes approach for bivariate binary responses. Under the assumption that the missing mechanism is missing at random (MAR), we have suggested methods to estimate the small area means along with the associated standard errors. Our findings have been supported by appropriate data analyses.