Robust Hotelling's T2 statistic based on M-estimator

Abstract

Hotelling's T 2 statistic is the multivariate generalization of the student's t-statistic. Hotelling's T 2 statistics is a method for testing hypotheses about multidimensional means. However, the classical Hotelling's T 2 statistic is very sensitive to the presence of outliers. In order to overcome this limitation, a modification is needed so that Hotelling's T 2 is robust. In this paper, classical Hotelling's T 2 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 T 2 statistic has been compared with the classical Hotelling's T 2 statistic and discussed in this paper to illustrate the advantage of modified Hotelling's T 2 statistic towards outliers. The performance of modified Hotelling's T 2 statistic is better than classical Hotelling's T 2 when number of sample, n and dimension, p is small.