On the robustness of Hotelling's T²

The influence of outliers in one of the samples on Hotelling's generalized T¹₀ is investigated by considering the directional derivate of the expected value with respect to the proportion of outliers in the disturbed population at the proportion zero. To make the problem tractable, the estimate of the covariance matrix thereby is replaced by its expected value under the altered distributional assumptions. For the two sample case the influence of outliers on the variance of the test criterion is also investigated. The analytical findings are confirmed by simulation results.