Detection of Multivariate Outliers in Elliptically Symmetric Distributions

Abstract

An extension of Ferguson's (Fourth Berkeley Symposium on Probability and Mathematical Statistics, 1961, Volume 1) univariate normal results and Schwager and Margolin's (1982) multivariate normal results for detection of outliers is made to the multivariate elliptically symmetric case with mean slippage. The main result can be viewed as a robustness property of the use of Mardia's multivariate kurtosis statistic as a locally optimum test statistic to detect outliers against nonnormal multivariate distributions.