Generalized principal Hessian directions for mixture multivariate skew elliptical distributions

Fei Chen, Lei Shi, Xuehu Zhu and Lixing Zhu

Journal of Multivariate Analysis, 2018, vol. 168, issue C, 142-159

Abstract: 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.

Keywords: Generalized principal Hessian directions; Principal Hessian directions; Skew elliptical distributions; Stein’s lemma; Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2018.07.006

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