Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 4 (2009), 99 -- 109## RIDGE REGRESSION ESTIMATOR: COMBINING UNBIASED AND ORDINARY RIDGE REGRESSION METHODS OF ESTIMATION

## Feras Sh. M. Batah and Sharad Damodar Gore

Abstract. Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR). This estimator is obtained from unbiased ridge regression (URR) in the same way that ordinary ridge regression (ORR) is obtained from ordinary least squares (OLS). Properties of MUR are derived. Results on its matrix mean squared error (MMSE) are obtained. MUR is compared with ORR and URR in terms of MMSE. These results are illustrated with an example based on data generated by Hoerl and Kennard [8].2000 Mathematics Subject Classification:62J05; 62J07.

Keywords:Multicollinearity; Ordinary Least Squares Estimator; Ordinary Ridge Regression Estimator; Unbiased Ridge Estimator

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Feras Shaker Mahmood BatahSharad Damodar Gore Department of Statistics, Department of Statistics, University of Pune, India. University of Pune, India. Department of Mathematics, e-mail: sdgore@stats.unipune.ernet.in. University of Alanber, Iraq. e-mail: ferashaker2001@yahoo.com