Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 344-362

MULTIVARIATE BAYESIAN SMALL AREA ESTIMATION: AN APPLICATION TO SURVEY AND SATELLITE DATA

By

G.S. DATTA, B. DAY, University of Georgia, Athens
and
DT. MAITI, University of Nebraska-Lincoln

SUMMARY. The importance of small area estimation in survey sampling is increasing, due to the growing demand for reliable small area statistics from both public and private sectors. Appropriate models are used to produce reliable small area estimates by ``borrowing strength" from neighboring areas. In many small area problems, data on related multiple characteristics and auxiliary variables are available. In this context, Fay (1987) proposed to borrow strength through multivariate modeling of related characteristics using a multiple regression model. The success of such modeling rests on the strength of dependence among these characteristics. In this article, we consider a superpopulation approach to hierarchical Bayes prediction of small area mean vectors using the multivariate nested error regression model of Fuller and Harter (1987). To compare the performance of the multivariate approach with the usual univariate approach we analyse the survey and satellite data of Battese {\em et al.} (1988) on crop areas under corn and soybean. Our simulations show that the multivariate approach may result in substantial improvement over its univariate counterpart. Finally, we obtain a set of necessary and sufficient conditions for the propriety of the posterior distributions corresponding to a certain class of improper priors on the components of variance matrices.

AMS (1991) subject classification.62D05, 62F15, 62H12, 62J05.

Key words and phrases. Components of variance, Gibbs sampling, multivariate mixed linear model, posterior predictive assessment, superpopulation, inverse Wishart distribution.

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