Advances in testing for multivariate outliers

Abstract

This paper reviews difficulties arising in the use of Wilks' multivariate outlier test statistic and examines various modifications. These include the use of highly robust estimators and the development of a sequential version for testing for an unspecified number of outliers. When the covariance matrix has a special structure, a suitably adapted likelihood ratio test statistic offers a substantial increase in power over Wilks' test. Union-intersection testing can also offer improved power, but only in restricted circumstances. It is concluded that the sequential test offers the best way of identifying outliers in multivariate normal samples when a formal test of significance is required.