Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 1, pp. 71--90

ADJUSTED BAYES ESTIMATORS WITH APPLICATIONS TO SMALL AREA ESTIMATION

By

MALAY GHOSH
* University of Florida, Gainesville*

and

TAPABRATA MAITI
* University of Nebraska-Lincoln*

*SUMMARY.* Much of the recent research on
small area estimation considers estimation of parameters of interest
simultaneously for several small or local areas. However, often the objective
is to classify these areas into multiple subgroups according to some
characteristic of interest, and identify those that are above or below certain
threshold values. The usual Bayes estimators, namely the posterior means are
often inadequate for such purposes, and need adjustment. In this article we
review mainly some of the continuing work on adjusted Bayes estimators so that
one can match the histogram of the posterior means with the histogram of the
population parameters. The resulting estimators need further adjustment if
one is interested also in the posterior means of the ranks. Some applications
of the general methods will be given.

*AMS (1991) subject classification.* 62D05, 62C10

*Key words and phrases. *
Constrained Bayes; exponential family; hierarchical Bayes;
empirical Bayes; Gibbs sampling; rank; regression; small area estimation.