A Comparison between Biased and Unbiased Estimators in Ordinary Least Squares Regression

Abstract

During the past years, different kinds of estimators have been proposed as alternatives to the Ordinary Least Squares (OLS) estimator for the estimation of the regression coefficients in the presence of multicollinearity. In the general linear regression model, Y = Xβ + e, it is known that multicollinearity makes statistical inference difficult and may even seriously distort the inference. Ridge regression, as viewed here, defines a class of estimators of β indexed by a scalar parameter k. Two methods of specifying k are proposed and evaluated in terms of Mean Square Error (MSE) by simulation techniques. A comparison is made with other ridge-type estimators evaluated elsewhere. The estimated MSE of the suggested estimators are lower than other estimators of the ridge parameter and the OLS estimator.