Abstract #302057

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JSM 2003 Abstract #302057
Activity Number: 205
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #302057
Title: Risk-Reducing Hierarchical Shrinkage for Generalized Linear Models
Author(s): Dan Spitzner*+
Companies: Virginia Polytechnic Institute and State University
Address: Department of Statistics, Blacksburg, VA, 24061,
Keywords: hierarchical models ; generalized linear models ; shrinkage estimation ; shrinkage estimation ; entropy loss
Abstract:

Motivated by normal-theory hierarchical solutions to the shrinkage estimation problem, a new, very simple class of prior distributions is presented for use in generalized linear models. The development is aimed directly at reducing risk, which is defined here for the general exponential family through entropy loss. Analysis relies extensively on asymptotic approximation and proceeds from general formulas provided in Smith (1999). The study produces closed-form estimator approximations, which are risk-reducing in their own right, insight into constructing prior densities, and risk diagnostics for use in practice. The new procedures are demonstrated on an existing epidemiology dataset.

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