Authors
Annaliisa Kankainen, Sara Taskinen, Hannu Oja
Publication date
2007/11/1
Journal
Statistical Methods and Applications
Volume
16
Issue
3
Pages
357-379
Publisher
Springer-Verlag
Description
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 …
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Scholar articles
A Kankainen, S Taskinen, H Oja - Statistical Methods and Applications, 2007