Generalized principal Hessian directions for mixture multivariate skew elliptical distributions
Generalized principal Hessian directions for mixture multivariate skew elliptical distributions
复制标题
混合多元偏椭圆分布的广义主 Hessian 方向
DOI：
10.1016/j.jmva.2018.07.006
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发表时间：
2018
影响因子：
1.6
通讯作者：
Zhu Lixing
中科院分区：
文献类型：
--
作者：
Chen Fei;Shi Lei;Zhu Xuehu;Zhu Lixing
基于Hessian矩阵的主Hessian方向（Principal Hessian direction, pHd）方法是一种基于矩的方法，由于其易于实现，是一种很有前途的充分降维方法。然而，它对预测器的分布有很强的条件，它必须是接近高斯分布的。本文研究了该方法是否适用于混合多元偏椭圆分布（MMSE），如果不适用，如何适应该技术。此外，我们提出了两种新的估计算法，用于扩展版本的pHd。这些理论结果也提醒研究者和使用者注意博士批判所依赖的理论条件。在有限样本情况下，对其性能进行了数值研究。
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.