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

Yanyuan Ma, Xinyu Zhang

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 - Jan 1 2015

Fingerprint

Information Criterion
Dimension Reduction
Sufficient Dimension Reduction
Model
Model Evaluation
Model Reduction
Goodness of fit
Linearity
Model Selection
Dimension reduction
Information criterion
selection methods
methodology

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

Cite this

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A validated information criterion to determine the structural dimension in dimension reduction models. / Ma, Yanyuan; Zhang, Xinyu.

In: Biometrika, Vol. 102, No. 2, 01.01.2015, p. 409-420.

Research output: Contribution to journalArticle

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