Proposition of new alternative tests adapted to the traditional T² test

Abstract

New alternative tests of the T² Hotelling’s test for testing hypotheses on the mean vector of a normal p-variate population were proposed. These tests were based on comedian robust estimator of the covariance matrix using an asymptotic T² distribution and a parametric bootstrap distribution to the null distribution of the statistical tests. The performance of these new tests was evaluated under normal and non-normal distributions through Monte Carlo simulations. The contaminated normal populations were also considered to evaluate the effects of outliers in performance of the tests. The type I error rats and power were computed in all Monte Carlo simulations by using the R software. The parametric bootstrap test based on the T² test statistic had equivalent performance of the T² original test. This test was recommended because it is easy to implement and computationally fast.