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.