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Robust sufficient dimension reduction via ball covariance

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  • Zhang, Jia
  • Chen, Xin

Abstract

Sufficient dimension reduction is an important branch of dimension reduction, which includes variable selection and projection methods. Most of the sufficient dimension reduction methods are sensitive to outliers and heavy-tailed predictors, and require strict restrictions on the predictors and the response. In order to widen the applicability of sufficient dimension reduction, we propose BCov-SDR, a novel sufficient dimension reduction approach that is based on a recently developed dependence measure: ball covariance. Compared with other popular sufficient dimension reduction methods, our approach requires rather mild conditions on the predictors and the response, and is robust to outliers or heavy-tailed distributions. BCov-SDR does not require the specification of a forward regression model and allows for discrete or categorical predictors and multivariate response. The consistency of the BCov-SDR estimator of the central subspace is obtained without imposing any moment conditions on the predictors. Simulations and real data studies illustrate the applicability and versatility of our proposed method.

Suggested Citation

  • Zhang, Jia & Chen, Xin, 2019. "Robust sufficient dimension reduction via ball covariance," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 144-154.
    • Handle: RePEc:eee:csdana:v:140:y:2019:i:c:p:144-154
    DOI: 10.1016/j.csda.2019.06.004
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    Cited by:

    1. Lili Xia & Tingyu Lai & Zhongzhan Zhang, 2023. "An Adaptive-to-Model Test for Parametric Functional Single-Index Model," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    2. Emmanuel Jordy Menvouta & Sven Serneels & Tim Verdonck, 2022. "Sparse dimension reduction based on energy and ball statistics," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 951-975, December.

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