Abstract #300654


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JSM 2002 Abstract #300654
Activity Number: 101
Type: Topic Contributed
Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300654
Title: Model selection and Shrinkage for Nearly Singular Designs
Author(s): Keith Knight*+
Affiliation(s): University of Toronto
Address: 100 St. George St., Toronto, Ontario, M5S 3G3, Canada
Keywords: regression ; model selection ; shrinkage ; asymptotic theory
Abstract:

We consider the problem of estimation in a linear model when the regressors are highly collinear in the sense that the design matrix always has full rank while its cross-product matrix tends to a singular matrix as the number of observations tends to infinity; we will call designs satisfying this latter condition "nearly singular." In such cases, it is well-known that least squares estimation is not particularly efficient, while penalized versions of least squares estimation, such as ridge regression, the Lasso (Tibshirani, 1996), AIC (Akaike, 1970), and SCAD (Fan & Li, 2001), can improve the efficiency. In this paper, we will examine the asymptotic behaviour of penalized least squares estimators as well as other shrinkage/selection estimators under the assumption that the design is nearly singular.


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