Robust hotelling's T2 statistic based on M-estimator

• Main Authors: Mohd Aizat Ahlam, Mohamad Mokhtar, Wan Nur Syahidah, Wan Yusoff, Chuan, Zun Liang
• Format: Conference or Workshop Item
• Language: English
• Published: IOP Publishing 2021
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/32784/1/Robust%20hotelling%E2%80%99s%20T2%20statistic%20based%20on%20M-estimator.pdf; http://umpir.ump.edu.my/id/eprint/32784/; https://doi.org/10.1088/1742-6596/1988/1/012116

Hotelling’s T2 statistic is the multivariate generalization of the student’s t statistic. Hotelling’s T2 statistic 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 T 2 statistic and discussed in this paper to illustrate the advantage of modified Hotelling’s T2 statistic towards outliers. The performance of modified Hotelling’s T 2 statistic is better than classical Hotelling’s T2 when number of sample, n and dimension, p is small.