Robust Hotelling’s T2 statistic based on M-estimator

Hotelling's T2 statistic is the multivariate generalization of the student's t-statistic. Hotelling's T2 statistics is a method for testing hypotheses about multidimensional means. However, the classical Hotelling's T2 statistic is very sensitive to the presence of outliers. In order to overcome this limitation, a modification is needed so that Hotelling's T2 is robust. In this paper, classical Hotelling's T2 statistic has been modified by substituting mean vector and covariance matrix with a robust estimator. M-estimator has been used for this modification. The performance of modified Hotelling's T2 statistic has been compared with the classical Hotelling's T2 statistic and discussed in this paper to illustrate the advantage of modified Hotelling's T2 statistic towards outliers. The performance of modified Hotelling's T2 statistic is better than classical Hotelling's T2 when number of sample, n and dimension, p is small.