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

• 成果类型: Article
• 署名作者: Ma, Yanyuan; Zhang, Xinyu
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Capital University of Economics & Business
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv004
• 发表日期: 2015
• 页码: 409420
• 关键词: sliced inverse regression; central subspace; Visualization

摘要

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.