JSM 2005 - Toronto

Abstract #302418

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 45
Type: Invited
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #302418
Title: Empirical and Hierarchical Bayes Estimation for Binary Response in Small Areas
Author(s): Karabi Sinha*+ and Malay Ghosh
Companies: University of Illinois, Chicago and University of Florida
Address: Department of Epidemiology and Biostatistics, Chicago, IL, 60612, USA
Keywords: Empirical Bayes ; Hierarchical Bayes ; Small Area Estimation ; NEF-QVF (natural exponential family with quadratic variance functions)
Abstract:

This work focuses on establishing EB and HB estimators in SAE for binary response. The motivation behind the work comes from analyzing data on health insurance, where the purpose is to estimate the proportion of individuals without health insurance in a given year for several small domains (cross-classified by age, gender, and other demographic characteristics) in minority subpopulations. For the entire U.S. population, the direct estimates for these domains, namely the sample proportions, are fairly reliable (since the sample size for each domain is reasonably large). However, when analysis is targeted toward specific subpopulations, such as Asians, Hispanics, and other similar minority sectors of the community where the sample size is not high, we run into the usual small-area problems and require developing indirect methods of estimation. In this paper, we employ both HB and EB methodologies to obtain estimates of these proportions and also the associated measures of precision. Results are derived in a general setup for the natural exponential family with quadratic variance functions and then specifically in the binary case with illustrations pertaining to the above-mentioned data.

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