TY - JOUR
T1 - Sufficient dimension reduction with mixture multivariate skew-elliptical distributions
AU - Guan, Yu
AU - Xie, Chuanlong
AU - Zhu, Lixing
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/1
Y1 - 2017/1
N2 - In inverse regression-based methodologies for sufficient dimension reduction, ellipticity (or slightly more generally, the linearity condition) of the predictor vector is a widely used condition, though there is concern over its restrictiveness. In this paper, Stein's Lemma is generalized to the class of mixture multivariate skewelliptical distributions in different scenarios to identify and estimate the central subspace. Within this class, necessary and sufficient conditions are explored for the simple covariance between the response (or its function) and the predictor vector to identify the central subspace. Further, we provides a way to do adjustments such that the central subspace can still be identifiable when this simple covariance fails to work. Simulations are used to assess the performance of the results and compare with existing methods. A data example is analysed for illustration.
AB - In inverse regression-based methodologies for sufficient dimension reduction, ellipticity (or slightly more generally, the linearity condition) of the predictor vector is a widely used condition, though there is concern over its restrictiveness. In this paper, Stein's Lemma is generalized to the class of mixture multivariate skewelliptical distributions in different scenarios to identify and estimate the central subspace. Within this class, necessary and sufficient conditions are explored for the simple covariance between the response (or its function) and the predictor vector to identify the central subspace. Further, we provides a way to do adjustments such that the central subspace can still be identifiable when this simple covariance fails to work. Simulations are used to assess the performance of the results and compare with existing methods. A data example is analysed for illustration.
KW - Central subspace
KW - Mixture multivariate skew-elliptical distributions
KW - Stein's Lemma
KW - Sufficient dimension reduction
UR - http://www3.stat.sinica.edu.tw/statistica/J27N1/J27N116/J27N116.html
UR - https://www.jstor.org/stable/44114374
UR - http://www.scopus.com/inward/record.url?scp=85011371112&partnerID=8YFLogxK
U2 - 10.5705/ss.202015.0274
DO - 10.5705/ss.202015.0274
M3 - Journal article
AN - SCOPUS:85011371112
SN - 1017-0405
VL - 27
SP - 335
EP - 355
JO - Statistica Sinica
JF - Statistica Sinica
IS - 1
ER -