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.

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