JSM 2004 - Toronto

Abstract #301655

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Activity Number: 116
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #301655
Title: Roles of Shrinkage Concepts in "Black Box'' Linear Models Analysis
Author(s): Dan Spitzner*+
Companies: Virginia Polytechnic Institute and State University
Address: Dept. of Statistics (0439), Blacksburg, VA, 24061,
Keywords: ridge regression ; model selection ; Bayesian model averaging ; continuum regression ; cross-validation ; information criteria
Abstract:

The roles of various shrinkage concepts are examined within a broad "black box'' framework, in which optimality of an objective function serves as the sole criterion for choice of estimator. Shrinkage concepts studied are: "shrinkage to a point,'' e.g., James-Stein and ridge regression; "shrinkage by dimension reduction,'' e.g., variable subset selection and Bayesian model averaging; and the "nonlinear shrinkage'' of continuum regression. These are studied under a broad range of both frequentist and empirical Bayes optimality criteria, in which the conventional framework is expanded to include weighted variations designed to match inferential goals such as prediction or parameter estimation. The study delineates a type of singularity by which dimension reduction contributes only slightly, if at all, to estimator performance, leaving "shrinkage to a point'' to act the main vehicle for optimality.

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