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Sufficient Dimension Reduction Through Independence and Conditional Mean Independence Measures

In: Festschrift in Honor of R. Dennis Cook

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  • Yuexiao Dong

    (Temple University, Department of Statistical Science)

Abstract

We propose a unified framework for sufficient dimension reduction through independence and conditional mean independence measures. When the interest is the conditional distribution of Y given X, α-distance covariance is used to recover the central space. If the focus is the conditional mean of Y given X, the central mean space can be estimated through α-martingale difference divergence. Compared with existing estimators based on the distance covariance which recover the central space, the new estimators are more accurate when the target is the central mean space. By choosing α smaller than one, the new estimators outperform existing estimators when the predictor distribution is heavy-tailed and when there is data contamination.

Suggested Citation

  • Yuexiao Dong, 2021. "Sufficient Dimension Reduction Through Independence and Conditional Mean Independence Measures," Springer Books, in: Efstathia Bura & Bing Li (ed.), Festschrift in Honor of R. Dennis Cook, pages 167-180, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-69009-0_8
    DOI: 10.1007/978-3-030-69009-0_8
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