Robust Hotelling’s T2 Statistic for Test a Hypothesis about Mean Population based on M-Estimator

Abstract

In this study, a robust estimator has been employed to replace the average vectors and correlation matrix in the traditional Hotelling's  statistic. This modification makes use of the M-estimator. In order to demonstrate the modified Hotelling's  statistic's advantage over the conventional Hotelling's  statistic with regard to anomalies, the behavior of the changed Hotelling's  statistic has indeed been compared to the standard Hotelling's  statistic and explained. Whenever the number of samples, n, and the dimensions, p, are minimal, the modified Hotelling's  statistic performs higher than the original Hotelling's .