Adaptive ridge estimator in a linear regression model with spherically symmetric error under constraint

Abstract

We consider adaptive ridge regression estimators in the general linear model with homogeneous spherically symmetric errors. A restriction on the parameter of regression is considered. We assume that all components are non negative (i.e. on the positive orthant). For this setting, we produce under general quadratic loss such estimators whose risk function dominates that of the least squares provided the number of regressors in the least fore.

Keywords:

• Adaptive ridge estimator
• positive orthant
• minimax
• quadratic loss
• risk function
• spherically symmetric distributions
• The James-Stein estimator

A.M.S. 2017 subject classification:

• primary 62H12
• secondary 62C20
• 62F10

Acknowledgment

Our warm thanks to the editor for reviewing our paper, who have generously given up his valuable time to the process of peer review, which led to an improved version of the paper.

Additional information

Funding

The research of both authors is totally funded by Cadi Ayyad University of Marrakesh – Kingdom of Morocco.