A Sequential Method to Search for Multiple Outliers in Multivariate Data

In usual multivariate analysis methods such as principal components, discriminant analysis and so on, the sample mean vector and covariance matrix are utilized. These can be strongly affected by the presence of only a few outliers. The problem of detecting outliers in multivariate data sets can be difficult because classical methods based on Mahalanobis distances may work well for identifying scattered outliers but perform poorly in the case of multiple clustered outliers. Methods based on robust Mahalanobis distances also do not perform well when the fraction of contamination or the dimension of data set is high and can also be computationally expensive. A method of detecting multiple outliers in multivariate data is proposed, which involves sequential testing of outliers and utilizes the leave-one-out approach at many stages. The proposed method is applied to several well-known data sets, and it is shown to perform better than many known methods of outlier detection, regardless of degree of contamination or dimension of the data set. It is also shown that it is marginally better to first obtain a clean sample to estimate the mean vector and covariance matrix and then apply classically efficient methods rather than using inefficient robust rules for estimation and subsequent outlier detection.