Robust Two-Sample Location Testing via Probability Measure Transform

This paper deals with the problem of testing for equality between the location parameters of two unknown symmetric distributions that may belong to different families. Under this framework, we develop a new robust extension of the two-sample Hotelling test (HT). 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 transform is structured by a non-negative function, called MT-function, that weights the data points. In the paper we show that proper selection of the involved MT-functions can result in significant enhancement of the decision performance in the presence of non-Gaussian distributions with heavy tails. The advantages of the proposed MT-HT are illustrated in simulation studies that involve synthetic measurements. Additionally, the MT-HT is illustrated for anomaly detection in a blurred and noisy video stream.