Risk-reducing shrinkage estimation for generalized linear models

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2005 · Volume 67 · Issue 1

DOI: 10.1111/j.1467-9868.2005.00495.x

Abstract

Summary.Empirical Bayes techniques for normal theory shrinkage estimation are extended to generalized linear models in a manner retaining the original spirit of shrinkage estimation, which is to reduce risk. The investigation identifies two classes of simple, all-purpose prior distributions, which supplement such non-informative priors as Jeffreys's prior with mechanisms for risk reduction. One new class of priors is motivated as optimizers of a core component of asymptotic risk. The methodology is evaluated in a numerical exploration and application to an existing data set.

Keywords

Entropy loss, Generalized linear models, Jeffreys's prior, Shrinkage estimation

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