Ridge Regression under Alternative Loss Criteria

T HE introduction by Hoerl and Kennard (1970) of a ridge regression estimator to deal with the problem of multicollinearity in regression has been followed by a large number of papers in the statistical literature. In the area of econometrics, though, the method of ridge regression has received little attention. I One of the reasons for the lack of interest in ridge regression on the part of the econometricians may be the fact that Hoerl and Kennard have justified their method on pragmatic grounds without providing any interpretation. Other reasons for the reluctant reception of ridge regression by econometricians are likely to include the difficulty in selecting a suitable value of the shrinking factor, which is important in securing a dominance over least squares, and the restrictive nature of the mean square error criterion, on which the claim of this dominance rests. In this paper we address all of these issues. The basic problem is that of estimating the coefficients of the standard linear regression model