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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.

Suggested Citation

  • 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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    1. Hee‐Seok Oh & Doug Nychka & Tim Brown & Paul Charbonneau, 2004. "Period analysis of variable stars by robust smoothing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 15-30, January.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, November.
    6. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    7. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    8. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    9. Lee, Jong Soo & Cox, Dennis D., 2010. "Robust smoothing: Smoothing parameter selection and applications to fluorescence spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3131-3143, December.
    10. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    11. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
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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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