Title: Principal Hessian directions for mixture multivariate skew elliptical distributions
Authors: Fei Chen - Yunnan University of Finance and Economics (China) [presenting]
Lei Shi - Yunnan University of Finance and Economics (China)
Lixing Zhu - Hong Kong Baptist University (Hong Kong)
Xuehu Zhu - Xi'an Jiaotong university (China)
Abstract: As a nice application of Stein's lemma, principal Hessian directions (pHd) using Hessian matrix is a moment-based method and becomes a promising methodology in sufficient dimension reduction because of its easy implementation. However, it requires strong conditions on the distribution of the predictors, which is very close to the normality assumption. Out of curiosity for its theoretical development and caution for its practical use, we investigate whether and how pHd is applicable when the distribution is mixture multivariate skew elliptical (MMSE) distribution and if not, how to derive a generalized pHd. Further, we propose two new estimation algorithms for the generalized pHd. Numerical studies are conducted to examine its performance in finite sample cases. The theoretical results also serves as a reminder for researchers and users to pay more attention to the theoretical conditions as pHd critically relies on them.