Hotelling's T ² when sampling from a contaminated normal rnodel: Robustness and outliers

In this paper, we study the robustness of Hotelling's T ² when sampling from a mixture of two multivariate normal distributions. First we investigate the robustness of the T ² statistic s test of the hypothesis H ₀: μ = 0 when the underlying distribution is the mixture of two normal populations. The effect on the actual significance level when the T ² test is used s a test of H ₀: μ ₁ = 0 in the presence of exactly r outliers from N _p(μ ₂, Σ) in a sample of size N is also considered.