Criteria for selection of response variables and the asymptotic properties in a multivariate calibration
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Let a set ofp responsesy=(y1,...yp)′ has a multivariate linear regression on a set ofq explanatory variablesx=(x1,...xq)′. Our aim is to select the most informative subset of responses for making inferences about an unknownx from an observedy. Under normality ony, two selection methods, based on the asymptotic mean squared error and on the Akaike's information criterion, are proposed by Fujikoshi and Nishii (1986,Hiroshima Math. J.,16, 269–277). In this paper, under a mild condition we will derive the cross-validation criterion and obtain the asymptotic properties of the three procedures.
Key wordsAIC calibration cross-validation multivariate linear regression variable selection
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