Research Article Open Access

A Modification of the Ridge Type Regression Estimators

Moawad El-Fallah Abd El-Salam1
  • 1 Department of Statistics and Mathematics and Insurance, Faculty of Commerce, Zagazig, University, Zagazig, Egypt


Problem statement: Many regression estimators have been used to remedy multicollinearity problem. The ridge estimator has been the most popular one. However, the obtained estimate is biased. Approach: In this stuyd, we introduce an alternative shrinkage estimator, called modified unbiased ridge (MUR) estimator for coping with multicollinearity problem. 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 estimator are derived. Results: The empirical study indicated that the MUR estimator is more efficient and more reliable than other estimators based on Matrix Mean Squared Error (MMSE).Conclusion: In order to solve the multicollinearity problem, the MUR estimator was recommended.

American Journal of Applied Sciences
Volume 8 No. 1, 2011, 97-102


Submitted On: 8 December 2010 Published On: 31 January 2011

How to Cite: El-Salam, M. E. A. (2011). A Modification of the Ridge Type Regression Estimators. American Journal of Applied Sciences, 8(1), 97-102.

  • 1 Citations



  • Multicollinearity
  • Ordinary Least Squares (OLS)
  • Ordinary Ridge Regression (ORR)
  • Unbiased Ridge Regression (URR)
  • Modified Unbiased Ridge (MUR)
  • Matrix Mean Squared Error (MMSE)
  • Cumulative Density Function (CDF)
  • ridge parameter
  • alternative shrinkage estimator
  • harmonic mean