A Bayes and Empirical Bayes Prediction for a Finite Population Total Using Auxiliary Information

• Activity Number: 290
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Mark Sebastian Hamner*+ and John Weldon Seaman and Dean M. Young and Melinda Miller Holt
• Companies: Texas State University and Baylor University and Baylor University and Texas Woman's University
• Keywords: superpopulation model ; finite population ; Bayesian inference ; total prediction

Abstract

The focus of this paper is on the prediction of a finite population total T by taking a sample of size n from a population of size N units. We assume that auxiliary information is known for each of the N population units. Cassel, Sarndal and Wretman (1976) employ classical sampling design theory, using inclusion probabilities and incorporate auxiliary information through a regression model to obtain the well-known general regression estimator. The regression model, however, is used only as a means to obtain an estimate of the coefficient vector. Hence, unbiasedness and variance expressions for their estimator are derived under the classical sampling design approach. In contrast, a superpopulation model provides the stochastic structure for Bayesian inference and establishes the main relations between the observed and unobserved units. Using a superpopulation model, we will obtain an empirical Bayesian estimator for the population total and show as a special case an emprical Bayesian analog to the general regression estimator. Further, we will present a special case fully Bayesian estimator to the general regression estimator.