where S2 is the usual unbiased estimator of (X2. This procedure in effect defines a new composite estimator which is a probabilistic mixture of bi and b1* and which has corresponding performance characteristics: its MSE is a weighted average (for given parameter values) of MSE bi and MSE bl*, the weights being given by the probabilities that inequality (13) will or will not be realized. We do not wish to suggest that time and effort be devoted to consideration of principal component estimators in every regression study. Benefits in terms of MSE reduction will often be nonexistent or outweighed by the additional computational costs. But in cases such that (i) data augmentation is impossible or very costly, (ii) multicollinearity is severe, and (iii) there exists a well-defined estimation objective, the principal component procedure appears to offer one route for improving upon conventional estimation techniques. FIGURE 1. BREAK-EVEN CORRELATION VALUES r 9