Outlier detection with the minimum covariance determinant estimator in practice

Robust statistics has slowly become familiar to all practitioners. Books entirely devoted to the subject are without any doubts responsible for the increased practice of robust statistics in all fields of applications. Even classical books often have at least one chapter (or parts of chapters) which develops robust methodology. The improvement of computing power has also contributed to the development of a wider and wider range of available robust procedures. However, this success story is now menacing to get backwards: non specialists interested in the application of robust methodology are faced with a large set of (assumed equivalent) methods and with over-sophistication of some of them. Which method should one use? How the (numerous) parameters should be optimaly tuned? These questions are not so easy to answer for non specialists! One could then argue that default procedures are available in most statistical softwares (Splus, R, SAS, Matlab,...). However, using as illustration the detection of outliers in multivariate data, it is shown that, on one hand, it is not obvious that one would feel confident with the output of default procedures, and that, on the other hand, trying to understand thoroughly the tuning parameters involved in the procedures might require some extensive research. This is not conceivable when trying to compete with the classical methodology which (while clearly unreliable) is so straightfoward.
The aim of the paper is to help the practitioners willing to detect in a reliable way outliers in a multivariate data set. The chosen methodology is the Minimum Covariance Determinant estimator being widely available and intuitively appealing.