OF FINANCIAL AND QUANTITATIVE ANALYSIS March 1978 SOME CLARIFYING COMMENTS ON DISCRIMINANT ANALYSIS 0

I. Prediction versus Stability A&E assert that our concept of prediction is not strictly applicable to the standard discriminant model because the latter does not explicitly incorporate a time dimension. If we pursue this point, we must conclude that either discriminant analysis should not be used in studies that require our concept of prediction or that special care must be taken in establishing the morphology of analysis to assure that claims of predictive classification success are bona fide. Presumably, A&E would agree with us that the former conclusion is unsatisfactory. In fact, one of the main tasks of our first paper was to address the latter conclusion. To complain that the standard discriminant model does not explicitly incorporate a time dimension is, in itself, an insufficient criticism. What is preferable is to also offer a normative solution to the problem, which we did in [4] . In a related comment, A&E point out that Lachenbruch [5] and Lachenbruch and Mickey [6] criticize the present use of holdout sample techniques. We have no quarrel with the approach proposed in the cited references. It is nonetheless true that the holdout sample technique is widely used in financial research, and it is the erroneous conclusion of "prediction" using contemporaneous holdout samples with which we took issue. A&E also note that prediction problems of relationship and parameter stability are not unique to discriminant analysis. We agree, so much so that we are surprised that the issue needs restatement or that erroneous claims of prediction still periodically appear in the literature. * Both, University of Kansas.