A Synchronized Ridge Regression Methodology with Extensions to Non-normal Problems

• Activity Number: 254
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Dan Spitzner*+
• Affiliation(s): Virginia Polytechnic Institute and State University/UNC-Chapel Hill
• Keywords: ridge regression ; cross-validation ; hierarchical Bayes ; exponential family regression

Abstract

Motivated by an ill-conditioned data set measuring the effects of air pollution on human mortality, the study explores ridge regression and various ridge parameter selection mechanisms, including cross validation and Bayesian approaches, in a general weighted framework. The advantage is that it permits consideration of a range of loss functions, and through a pre-analysis aimed at diagnosing risk even multiple loss functions at the same time. The study provides a framework that synchronizes the most common approaches to ridge parameter selection and enough flexibility to yield a parallel methodology for exponential family regression models.

The development stems from ridge regression's asymptotic connections with classical James-Stein estimation, also treated in a weighted form, and asymptotic evaluation of risk. The extension to non-normal regression uses entropy loss to evaluate estimators and relies heavily on Bayesian hierarchical modeling for their construction.