A QUADRATIC MODEL FOR MULTIVARIATE PREDICTION.
HARVARD UNIV CAMBRIDGE MASS
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A step is taken toward the development of non-linear models for multivariate prediction. The usual method for constructing a predictor function involves fitting a linear combination of the predictand independent variables which minimize the mean square error m.s.e. of prediction. The justification given for this method is that although the true relation among the variables is probably not a linear one, the linear function is a reasonable approximation locally. To obtain a non-linear prediction model consider the following in addition to the best linear predictor b.l.p. for the predictand dependent variable compute the b.l.p. for the square of the predictand. Then if X denotes the predictand we have, for each set of observations on the independent variables, a linear prediction for X and a linear prediction for X-squared. The present work is concerned with methods of combining these two predictions to yield a single prediction for X. The hope, of course, is that this new predictor will represent an improvement.