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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.
Acknowledgements
The authors would like to thank the Editor, an Associate Editor and a referee for their valuable comments, which lead to a greatly improved paper.
Conflict of interest disclosure statement
No potential conflict of interest was reported by the authors.
Funding
Xue's work was supported in part by NSF-China grants [11401095], [71401037] and Program for Innovative Research Team at UIBE [CXTD5-05]. Yin's work was supported in part by a NSF grant [1205546].