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Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects

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  • Yuan Xue
  • Xiangrong Yin

Abstract

In this paper, we introduce sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects, which suggests a new concept of central T dimension folding subspace (CTDFS). CTDFS includes central dimension folding subspace and central mean dimension folding subspace as special cases. A class of estimation methods on CTDFS is introduced. In particular, we focus on sufficient dimension folding for robust functionals. In this paper, we pay special attention to the central quantile dimension folding subspace (CQDFS), a widely interesting case of CTDFS, and develop new estimation methods. The performances of the proposed estimation methods on estimating the CQDFS are demonstrated by simulations and by analysing the primary biliary cirrhosis data.

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  • Yuan Xue & Xiangrong Yin, 2015. "Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 253-269, June.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:253-269
    DOI: 10.1080/10485252.2015.1022176
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    Cited by:

    1. Xue, Yuan & Yin, Xiangrong & Jiang, Xiaolin, 2016. "Ensemble sufficient dimension folding methods for analyzing matrix-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 193-205.

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