A monte carlo comparison of some ridge and other biased estimators

Abstract

A comparative study of the performance of 8 ridge estimators, 5 other biased estimators, and the Ordinary Least Squares estimate is made through a Monte Carlo experiment. The control parameters used in the simulation study are:(1)A measure of the degree of multicollinearity in X,(2)The number of independent variables,(3)The variance of the error term(for unit length parameter vector β), and(4)The most favorable and the least favorable choices of β(as defined by McDonald and Galarneau). 100 replications are run on each combination of a 6Z×3×5×2 factorial design, using sample sizes of n=100. The empirical mean squared error as well as some other properties of the sampling distributions of the squared loss are reported for the estimators considered.

Keywords:

• Ridge Estimator
• Biased Estimator
• Ordinary Least Squares
• Multicollinearity
• Squared Loss
• MSE

†Amitava Mitra is Assistant Professor, University of Southern California-Eastern Region, Systems Management Department, 5510 Columbia Pike, Arlington, Va. 22204. Robert F. Ling is Professor, Department of Mathematical Sciences, Clemson University, Clemson, S.C. 29631. Research was supported in part by the Office of Naval Research under Contract N00014-75-C-0451

†Amitava Mitra is Assistant Professor, University of Southern California-Eastern Region, Systems Management Department, 5510 Columbia Pike, Arlington, Va. 22204. Robert F. Ling is Professor, Department of Mathematical Sciences, Clemson University, Clemson, S.C. 29631. Research was supported in part by the Office of Naval Research under Contract N00014-75-C-0451

Notes

†Amitava Mitra is Assistant Professor, University of Southern California-Eastern Region, Systems Management Department, 5510 Columbia Pike, Arlington, Va. 22204. Robert F. Ling is Professor, Department of Mathematical Sciences, Clemson University, Clemson, S.C. 29631. Research was supported in part by the Office of Naval Research under Contract N00014-75-C-0451