A Robust Hotelling’s T2 Test Using Minimum Covariance Determinant Estimator

Abstract

Hotelling’s T2 statistic is a good statistic for inference about the mean of a multivariate normal population. In Hotelling’s T2 statistic, approximation with Bonferroni confidence intervals provides shorter interval than T2 confidence intervals. Therefore, to find the mean of a multivariate normal population, simultaneous t-intervals based on the Bonferroni method is often applied. However, hypothesis test and confidence intervals based on T2 statistic can be significantly affected by outliers in a set of multivariate normal data. Therefore, to find a good estimator for the mean of a multivariate normal population, the Minimum Covariance Determinant (MCD) estimator is used. To increase the efficiency of the MCD estimator, this test statistic is applied using the reweighted MCD which gives weights to the mean and covariance based on the robust of the observations.