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Predictive Mean Square Error and Stochastic Regressor Variables

Subhash C. Narula
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 23, No. 1 (1974), pp. 11-17
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2347047
Stable URL: http://www.jstor.org/stable/2347047
Page Count: 7
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Predictive Mean Square Error and Stochastic Regressor Variables
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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.

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