Tests of multinormality based on location vectors and scatter matrices
Tests of multinormality based on location vectors and scatter matrices
复制标题
基于位置向量和散点矩阵的多重正态性检验
DOI：
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发表时间：
2007
期刊：
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通讯作者：
H. Oja
中科院分区：
文献类型：
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作者：
A. Kankainen;S. Taskinen;H. Oja
经典的单变量非对称性测量，如Pearson（均值-中位数）/σ或（均值-众数）/σ，通常测量两个独立位置参数之间的标准化距离，并已广泛用于评估单变量正态性。类似地，单变量峰度的度量通常只是两个尺度度量的比值。以经典的标准化四阶矩和平均偏差与标准偏差的比率为例。在本文中，我们考虑多正态性的测试是基于两个多变量位置向量估计之间的马氏距离或两个散布矩阵估计之间的（矩阵）距离，分别。渐近理论的发展提供近似零分布，以及考虑渐近效率。计算了污染正态分布连续序列的极限皮特曼效率，并将其与Mardia的经典检验进行了比较。模拟是用来比较有限的样本效率。最后通过一个实例说明了该理论。
Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is developed to provide approximate null distributions as well as to consider asymptotic efficiencies. Limiting Pitman efficiencies for contiguous sequences of contaminated normal distributions are calculated and the efficiencies are compared to those of the classical tests by Mardia. Simulations are used to compare finite sample efficiencies. The theory is also illustrated by an example.