TY - JOUR
T1 - Generalized principal Hessian directions for mixture multivariate skew elliptical distributions
AU - Chen, Fei
AU - Shi, Lei
AU - Zhu, Xuehu
AU - Zhu, Lixing
N1 - Funding Information:
The research presented herein was supported by a grant from the University Grants Council of Hong Kong, China ( HKBU12303115 ) and grants from the National Natural Science Foundation of China (Grant Nos. 11661078 , 11671042 , 11261064 and 11561071 ). F. Chen was also a visiting scholar at Hong Kong Baptist University supported by the KC Wong Education Foundation . The authors thank the Editor-in-Chief, the Associate Editor and referees for their constructive comments and suggestions that led to an improvement of an early draft of this paper.
PY - 2018/11
Y1 - 2018/11
N2 - Principal Hessian directions (pHd) based on the Hessian matrix is a moment-based method and a promising methodology for sufficient dimension reduction because of its easy implementation. However, it requires strong conditions on the distribution of the predictors, which must be nearly Gaussian. We investigate here whether and how this method is applicable when the distribution is a mixture multivariate skew elliptical (MMSE) distribution, and if not, how to adapt the technique. Further, we propose two new estimation algorithms for an extended version of pHd. The theoretical results also serve as a reminder for researchers and users to pay attention to the theoretical conditions on which pHd critically relies. Numerical studies are conducted to examine its performance in finite-sample cases.
AB - Principal Hessian directions (pHd) based on the Hessian matrix is a moment-based method and a promising methodology for sufficient dimension reduction because of its easy implementation. However, it requires strong conditions on the distribution of the predictors, which must be nearly Gaussian. We investigate here whether and how this method is applicable when the distribution is a mixture multivariate skew elliptical (MMSE) distribution, and if not, how to adapt the technique. Further, we propose two new estimation algorithms for an extended version of pHd. The theoretical results also serve as a reminder for researchers and users to pay attention to the theoretical conditions on which pHd critically relies. Numerical studies are conducted to examine its performance in finite-sample cases.
KW - Generalized principal Hessian directions
KW - Principal Hessian directions
KW - Skew elliptical distributions
KW - Stein's lemma
KW - Sufficient dimension reduction
UR - http://www.scopus.com/inward/record.url?scp=85050681885&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2018.07.006
DO - 10.1016/j.jmva.2018.07.006
M3 - Journal article
AN - SCOPUS:85050681885
SN - 0047-259X
VL - 168
SP - 142
EP - 159
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -