A Hotelling Test Based on MCD

Abstract

Hypothesis tests and confidence intervals based on the classical Hotelling T 2 statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator of Rousseeuw (1984) instead of the classical mean and covariance matrix. The distribution of this new statistic differs from the classical one. Similarly to the classical T 2 distribution, we obtain a multiple of a certain F-distribution. It is shown through a Monte Carlo study that this approximation is very accurate, both at the normal model and at contamination models.