TY - JOUR
T1 - Generalized kernel-based inverse regression methods for sufficient dimension reduction
AU - Xie, Chuanlong
AU - Zhu, Lixing
N1 - Funding Information:
Lixing Zhu is a professor of Center for Statistics and Data Science at Beijing Normal University, Zhuhai, China and a Chair professor of Department of Mathematics at Hong Kong Baptist University, Hong Kong, China. His research described herewith was supported by a grant from the University Grants Council of Hong Kong, Hong Kong, China and a grant from the National Natural Science Foundation of China (NSFC11671042)..
PY - 2020/10
Y1 - 2020/10
N2 - The linearity condition and the constant conditional variance assumption popularly used in sufficient dimension reduction are respectively close to elliptical symmetry and normality. However, it is always the concern about their restrictiveness. In this article, we give systematic studies to provide insight into the reasons why the popularly used sliced inverse regression and sliced average variance estimation need these conditions. Then we propose a new framework to relax these conditions and suggest generalized kernel-based inverse regression methods to handle a class of mixture multivariate unified skew-elliptical distributions.
AB - The linearity condition and the constant conditional variance assumption popularly used in sufficient dimension reduction are respectively close to elliptical symmetry and normality. However, it is always the concern about their restrictiveness. In this article, we give systematic studies to provide insight into the reasons why the popularly used sliced inverse regression and sliced average variance estimation need these conditions. Then we propose a new framework to relax these conditions and suggest generalized kernel-based inverse regression methods to handle a class of mixture multivariate unified skew-elliptical distributions.
KW - Stein's Lemma
KW - Sufficient dimension reduction
KW - Unified skew-elliptical distribution
UR - http://www.scopus.com/inward/record.url?scp=85084834931&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2020.106995
DO - 10.1016/j.csda.2020.106995
M3 - Journal article
AN - SCOPUS:85084834931
SN - 0167-9473
VL - 150
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
M1 - 106995
ER -