A Quasi-Empirical Bayes Method for Small Area Estimation

Abstract

This article develops an empirical Bayes-type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data. The objective of the analysis is to draw inference about the intermediate or the random means. We combine the quasi-likelihood functions to construct the quasi-posterior density of the random means conditional on the data and the marginal parameters. We describe a method for estimating the marginal parameters that are then substituted in the quasi-posterior density of the random means. The empirical quasi-posterior density so derived is used to obtain the quasi-empirical Bayes estimates of the random parameters. We apply the methodology to estimate the utilization rates of cancer chemotherapy for the selected counties in the state of Washington.

Key Words:

• Estimating equations
• Generalized EM algorithm
• Jackknife
• Marginal likelihood
• Method of moments