The effect of nonnormality on some multivariate tests and robustness to nonnormality in the linear model
The effect of nonnormality on some multivariate tests and robustness to nonnormality in the linear model
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DOI：
10.1093/biomet/58.1.105
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发表时间：
1971-04
期刊：
影响因子：
2.7
通讯作者：
K. Mardia
中科院分区：
文献类型：
--
作者：
K. Mardia
摘要 按照 Box 和 Watson (1962) 的方法，研究了非正态性对多元回归检验、单向多元方差分析和协方差矩阵相等性检验的影响。在非正态情况下，导出多元回归问题的广义马哈拉诺比斯距离类型统计量的分布的近似值。结果表明，多变量观测值对非正态性的敏感性是由回归量的非正态性程度决定的。推导了广义马氏距离的随机化分布。方差的多变量分析被发现对非正态性具有鲁棒性，而协方差矩阵相等性的检验对非正态性敏感。给出了对非正态性的这种不同程度的敏感度的解释。
SUMMARY The effect of nonnormality on multivariate regression tests, on thle one-way multivariate analysis of variance and on tests of equality of covariance matrices is studied following the approach of Box & Watson (1962). In the nonnormal case, an approximation to the distribution of a generalized Mahalanobis distance type of statistic for the multivariate regression problem is derived. It is shown that sensitivity to nonnormality in the multivariate observations is determined by the extent of nonnormality of the regressors. The randomization distribution of the generalized Mahalanobis distance is deduced. The multivariate analysis of variance is found to be robust to nonnormality whereas the tests for equality of covariance matrices are found to be sensitive to nonnormality. An explanation for this varying degree of sensitivity to nonnormality is given.