On the ridge regression estimator with sub-space restriction

ABSTRACT

In the linear regression model with elliptical errors, a shrinkage ridge estimator is proposed. In this regard, the restricted ridge regression estimator under sub-space restriction is improved by incorporating a general function which satisfies Taylor’s series expansion. Approximate quadratic risk function of the proposed shrinkage ridge estimator is evaluated in the elliptical regression model. A Monte Carlo simulation study and analysis based on a real data example are considered for performance analysis. It is evident from the numerical results that the shrinkage ridge estimator performs better than both unrestricted and restricted estimators in the multivariate t-regression model, for some specific cases.

KEYWORDS:

• Approximate risk
• elliptically contoured distribution
• linear regression model
• restricted estimator
• shrinkage estimator
• ridge estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62F15
• Secondary: 62H05

Acknowledgments

We would like to thank the anonymous reviewer for his/her valuable comments and suggestions which improved the quality of this work.