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

Yanyuan Ma, Xinyu Zhang

Research output: Contribution to journalArticle

11 Scopus citations

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

Original languageEnglish (US)
Pages (from-to)409-420
Number of pages12
JournalBiometrika
Volume102
Issue number2
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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