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Generalized principal Hessian directions for mixture multivariate skew elliptical distributions

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

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.

Suggested Citation

  • Chen, Fei & Shi, Lei & Zhu, Xuehu & Zhu, Lixing, 2018. "Generalized principal Hessian directions for mixture multivariate skew elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 142-159.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:142-159
    DOI: 10.1016/j.jmva.2018.07.006
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    References listed on IDEAS

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    Cited by:

    1. Xie, Chuanlong & Zhu, Lixing, 2020. "Generalized kernel-based inverse regression methods for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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