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Diagnostic studies in sufficient dimension reduction

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  • Xin Chen
  • R. Dennis Cook
  • Changliang Zou

Abstract

Sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information. Numerous dimension reduction methods have been developed based on this paradigm. However, little effort has been devoted to diagnostic studies within the context of dimension reduction. In this paper we introduce methods to check goodness-of-fit for a given dimension reduction subspace. The key idea is to extend the so-called distance correlation to measure the conditional dependence relationship between the covariates and the response given a reduction subspace. Our methods require minimal assumptions, which are usually much less restrictive than the conditions needed to justify the original methods. Asymptotic properties of the test statistic are studied. Numerical examples demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Xin Chen & R. Dennis Cook & Changliang Zou, 2015. "Diagnostic studies in sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 102(3), pages 545-558.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:545-558.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv016
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    Cited by:

    1. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    2. Zhang, Yaowu & Zhou, Yeqing & Zhu, Liping, 2024. "A post-screening diagnostic study for ultrahigh dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).

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