A validated information criterion to determine the structural dimension in dimension reduction models

Yanyuan Ma and Xinyu Zhang

Biometrika, 2015, vol. 102, issue 2, 409-420

Abstract: A crucial component of performing sufficient dimension reduction is to determine the structural dimension of the reduction model. We propose a novel information criterion-based method for this purpose, a special feature of which is that when examining the goodness-of-fit of the current model, one needs to perform model evaluation by using an enlarged candidate model. Although the procedure does not require estimation under the enlarged model of dimension k+1, the decision as to how well the current model of dimension k fits relies on the validation provided by the enlarged model; thus we call this procedure the validated information criterion, vic(k). Our method is different from existing information criterion-based model selection methods; it breaks free from dependence on the connection between dimension reduction models and their corresponding matrix eigenstructures, which relies heavily on a linearity condition that we no longer assume. We prove consistency of the proposed method, and its finite-sample performance is demonstrated numerically.

Date: 2015
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Citations: View citations in EconPapers (7)

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