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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.

Proposition of new alternative tests adapted to the traditional T 2 test