Abstract.
Hotelling's T 2 statistic is an important tool for inference about the center of a multivariate normal population. However, hypothesis tests and confidence intervals based on this statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator [9] instead of the classical mean and covariance matrix. Recently, a fast algorithm was constructed to compute the MCD [10]. In our test statistic we use the reweighted MCD, which has a higher efficiency. The distribution of this new statistic differs from the classical one. Therefore, the key problem is to find a good approximation for this distribution. Similarly to the classical T 2 distribution, we obtain a multiple of a certain F-distribution. A Monte Carlo study shows that this distribution is an accurate approximation of the true distribution. Finally, the power and the robustness of the one-sample test based on our robust T 2 are investigated through simulation.
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Willems, G., Pison, G., Rousseeuw, P. et al. A robust Hotelling test. Metrika 55, 125–138 (2002). https://doi.org/10.1007/s001840200192
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DOI: https://doi.org/10.1007/s001840200192