Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 3, pp. 402--416



PATRICK J. FARRELL, Carleton University, Ottawa, Canada

SUMMARY. Direct survey estimators for small areas are often unstable due to the small (or nonexistent) samples taken from these areas. Estimators with less variability can be derived by "borrowing strength" from related areas. In this study, a hierarchical Bayes methodology for estimating small area proportions is proposed. The idea consists of incorporating random effects which reflect the structure of the sample design into a logistic regression model. A data example involving the estimation of local labour force participation rates is presented. Comparisons are drawn with an empirical Bayes approach used by Farrell, MacGibbon, and Tomberlin (1997a), and an analogous procedure which incorporates a modification to the Laird and Louis (1987) Type III bootstrap suggested by Carlin and Gelfand (1991).

AMS (1991) subject classification. Primary 62D05; secondary 62F15.

Key words and phrases. Empirical Bayes estimation, Gibbs sampling, hierarchical Bayes estimation, labour force participation, logistic regression, random effects models.

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