Shrinkage structure in biased regression

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Druilhet, Pierre¹  Mom, Alain^2,3 

[1] CREST ENSAI, F-35170 Bruz, France

[2] Univ Rennes 2, Rennes, France

[3] Univ Rennes 1, IRMAR, F-35042 Rennes, France

关键词: Biased regression;    Regression on components;    Shrinkage factors;    Signal-to-noise ratio;    James-Stein estimator;   

DOI  :  10.1016/j.jmva.2006.06.011

来源: Elsevier

【 摘 要 】

Biased regression is an alternative to ordinary least squares (OLS) regression, especially when explanatory variables are highly correlated. In this paper, we examine the geometrical structure of the shrinkage factors of biased estimators. We show that, in most cases, shrinkage factors cannot belong to [0, 1] in all directions. We also compare the shrinkage factors of ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLSR) in the orthogonal directions obtained by the signal-to-noise ratio (SNR) algorithm. In these directions, we find that PLSR and RR behave well, whereas shrinkage factors of PCR have an erratic behaviour. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free