Empirical Bayes estimation
M. Ghosh, Glen D. Meeden · 2021
Empirical and hierarchical Bayes methods are becoming increasingly popular in statistics, especially in the context of simultaneous estimation of several parameters. For example, agencies of the Federal Government have been involved in obtaining estimates of per capita income, unemployment rates, crop yields and so forth for many state and local government areas. In such situations, quite often estimates of certain area means, or simultaneous estimates of several area means, can be improved by incorporating information from similar neighbouring areas. Estimation problems of this type are usually referred to as small area estimation problems. The chapter considers simultaneous estimation of means from several strata when only a few observations are available from each individual stratum. In actual surveys, however, auxiliary information exists, judicious use of which can lead to estimators with enhanced precision when compared to the direct survey estimators.