A modified approach to small area estimation.

Abstract

The ever-growing need for good estimates of the health, social, political, and economic parameters of local areas has served as the motivating force for new developments in methodology. Due to the constraints of sample size, design, and cost, accessible data from large areas for criterion variables of interest is often used jointly with local data on symptomatic variables. Furthermore, several procedures have derived local area estimators by combining symptomatic information and sample data into a multiple regression format. In those situations where assumptions are too strict or unrealistic, as when a nonlinear model is more appropriate, the merits of a more flexible approach are obvious. Our research focuses upon a further investigation of an alternative strategy for which the most limiting assumption is the availability of good symptomatic information. A more formal representation of the model is developed within the framework of a poststratification scheme. The methodology involves ratio estimation of the respective stratum means via indicator variables which serve the purpose of classification. To determine the accuracy of the proposed small area estimator and allow for comparisons of precision with respect to other strategies, we express the relationship between criterion and symptomatic variables by relevant continuous multivariate distributions. Specifically, comparisons are made with the results obtained using a regression estimator which is applicable to the same general setting. The theoretical framework considers multivariate stratification, where boundary determination is achieved by application of practical methods which use minimum variance stratification as a criterion.