Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality
Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality
复制标题
高维数据多元三阶矩估计及其在检验多元正态性中的应用
DOI：
10.1007/s00180-018-00865-9
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发表时间：
2019
影响因子：
1.3
通讯作者：
Himeno Tetsuto
中科院分区：
文献类型：
--
作者：
Yamada Takayuki;Himeno Tetsuto
本文研究了多元三阶矩及其估计问题。Mardia（Biometrika 57：519-530，1970）和Srivastava（Stat Probab Lett 2：263-267，1984）独立地提出了多元偏度及其估计量。然而，这些估计不能定义的情况下，其中的维数p大于样本大小N。在本文中，我们处理多元三阶矩\gamma γ 它是由观测向量的Hadamard积定义的，并提出了$$\gamma $$的估计 γ 当$$p>N$$时， p > N .基于该估计量，我们提出了一种新的多元正态性检验方法。在零假设下，检验统计量是渐近标准正态的，这得到了Monte Carlo模拟的支持。我们计算一些经验功效来查看测试的性能。
This paper is concerned with the multivariate 3rd moment and its estimation. Mardia (Biometrika 57:519–530, 1970) and Srivastava (Stat Probab Lett 2:263–267, 1984) proposed the multivariate skewness and its estimator, independently. However, these estimators cannot be defined for the case in which the dimensionpis larger than the sample sizeN. In this paper, we treat the multivariate 3rd moment $$\gamma $$ γ which is defined by using Hadamard product of observation vectors, and propose an estimate of $$\gamma $$ γ which is well defined when $$p>N$$ p > N . Based on the estimator, we propose a new test for multivariate normality. Under the null hypothesis, the test statistic is asymptotically standard normal, which is supported by Monte Carlo simulations. We calculate some empirical powers to see the performance of the test.