Generalized principal Hessian directions for mixture multivariate skew elliptical distributions

Fei Chen, Lei Shi, Xuehu Zhu, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)142-159
Number of pages18
JournalJournal of Multivariate Analysis
Publication statusPublished - Nov 2018

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Generalized principal Hessian directions
  • Principal Hessian directions
  • Skew elliptical distributions
  • Stein's lemma
  • Sufficient dimension reduction


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