Predictive Mean Square Error and Stochastic Regressor Variables

Subhash C. Narula

Journal of the Royal Statistical Society Series C, 1974, vol. 23, issue 1, 11-17

Abstract: When prediction is the main objective, predictive mean square error (p.m.s.e.) seems to be a more reasonable criterion. Here we consider two approaches to improve the p.m.s.e. of the predicted response when predictor variables are stochastic and, in particular, follow a multivariate normal distribution. The first technique, the subset approach, uses only a subset of the available predictor variables to predict the response. A decision rule to select the subset is given. In the second method, the lambda approach, the regression coefficients are scaled down by a suitable constant. An estimator of the constant is suggested. Both techniques are illustrated by an example.

Date: 1974
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