Measure-Transformed Two-Sample Hotelling Test

In this paper, a new robust extension of the two-sample Hotelling test (HT) is developed. The proposed extension, called measure-transformed HT (MT-HT), operates by applying a transform to the probability measures of some reshaped versions of the two compared data sets. The considered measure transformation is structured by a non-negative data-weighting function, called MT-function. We show that proper selection of the involved MT-functions can lead to significant enhancement of the decision performance in the presence of heavy-tailed data. Simulation study illustrates the advantages of the proposed test compared to the two-sample HT and other robust extensions.

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