A robust test approach for equality of mean vectors of two independent groups under the multivariate Behrens-Fisher problem

Abstract

In multivariate statistical inference, the Hotelling $T^2$ statistic is used to test the equality of mean vectors for two independent groups. This statistic needs the multivariate normality and homogeneous covariance matrices assumptions. However, homogeneous covariance matrices assumption may not be provided in real applications. This case is called the multivariate Behrens-Fisher problem. There are several studies to test the equality of two mean vectors for the independent groups under the multivariate Behrens-fisher problem. But these studies do not interest in outliers at data sets. In this study, we propose solving problems caused by multivariate Behrens-Fisher and outliers in the dataset. We compare our proposed approach with other approaches regarding empirical size and power at simulated data that are both uncontaminated and contaminated. Thus we show that our proposed approach can be used to test the equality of mean vectors for two independent groups under multivariate Behrens-Fisher problem without being affected by outliers in the data. Moreover, we construct an R function in the MVTests package to use our proposed approach for real data applications.

Keywords:

• Computational approach test
• Hotelling multivariate Behrens-Fisher problem
• RobCat function
• Robust test approach
• ${\mathrm{T}}^2$

Acknowledgements

This work has been enhanced from Gülnur Karaosman’s master’s thesis and has received financial assistance from the Ondokuz Mayıs University Project Management Office under the designation of Project Number PYO.FEN.1904.21.015.

Disclosure statement

No potential conflict of interest was reported by the authors.