The sampling design and sample size of most large scale national surveys are usually determined so as to produce a national estimate of a parameter of interest with a desired level of precision. Quite often there is a need to produce similar estimates with the same level of precision for certain subnational regions (such as states or counties). However, the small samples associated with subnational regions do not produce reliable estimates. Problems of this kind are known as small area estimation problems. Reliable small area statistics are needed by various federal and local government agencies for policy making and the allocation of funds. The empirical Bayes (EB) and hierarchical Bayes (HB) methods have been widely used to produce small area statistics. These methods use explicit hierarchical models to borrow strength from related resources. This research extends the empirical Bayes (EB) and hierarchical Bayes (HB) methods to address the following issues in small area estimation: (1) Measurement errors in survey responses; (2) Small area statistics from a dual-frame sampling design; and (3) Estimation of small sample means under exponential power distributions.
