A simulation study of biased estimators against the ordinary least squares estimator

C Thiart Department of Statistical Sciences, University of Cape Town, Rondebosch, 7700, South Africa

T.T Dunne Department of Statistical Sciences, University of Cape Town, Rondebosch, 7700, South Africa

C.G Troskie Department of Statistical Sciences, University of Cape Town, Rondebosch, 7700, South Africa

D.O Chalton Department of Statistical Sciences, University of Cape Town, Rondebosch, 7700, South Africa

Abstract

A simulation study was performed to examine the relative efficiency of thirteen estimators against OLSE across thirty combinations of orientation, variance and known parameter vector, encompassing several different degrees of collinearity. Estimation procedures include principal components, ridge and generalized ridge, jackknife, shrinkage and fractional principalcomponent methods. Overall, in the face of collinearity the biased estimators perform better than OLSE, but no 'optimal' estimator emerges, and a suitable choice of estimator will depend on the circumstances

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A simulation study of biased estimators against the ordinary least squares estimator