The Annals of Statistics

Good and Optimal Ridge Estimators

R. L. Obenchain

Full-text: Open access

Abstract

In generalized ridge estimation, the components of the ordinary least squares (OLS) regression coefficient vector which lie along the principal axes of the given regressor data are rescaled using known ridge factors. Generalizing a result of Swindel and Chapman, it is shown that, if each ridge factor is nonstochastic, nonnegative, and less than one, then there is at most one unknown direction in regression coefficient space along which ridge coefficients have larger mean squared error than do OLS coefficients. Then, by decomposing the mean squared error of a ridge estimator into components parallel to and orthogonal to the unknown true regression coefficient vector, new insight is gained about definitions for optimal factors. Estimators of certain unknown quantities are displayed which are maximum likelihood or unbiased under normal theory or which have correct range.

Article information

Source
Ann. Statist., Volume 6, Number 5 (1978), 1111-1121.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344314

Digital Object Identifier
doi:10.1214/aos/1176344314

Mathematical Reviews number (MathSciNet)
MR518957

Zentralblatt MATH identifier
0384.62059

JSTOR
links.jstor.org

Subjects
Primary: 62J05: Linear regression
Secondary: 62F10: Point estimation

Keywords
Ridge regression mean squared error optimality

Citation

Obenchain, R. L. Good and Optimal Ridge Estimators. Ann. Statist. 6 (1978), no. 5, 1111--1121. doi:10.1214/aos/1176344314. https://projecteuclid.org/euclid.aos/1176344314


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