A note on some conditions for optimality of certain ridge estimators

Consider the linear regression model, y = Xβ + ε in the usual notation with X'X being in the correlation form. Galpin(1980) claimed that the ridge estimators of Hoerl, Kennard and Baldwin(1975) and Lawless and Wang(1976) give guaranteed lower mean squared error than the least squares estimator when X'X has at least two very small eigen values. We show that the arguments of Galpin(1980) leading to the above claim are incorrect, and hence the claim itself is unsubstantited. A Monte Carlo study shows that Galpin's claim is not correct in general.