A robust Hotelling test |
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Authors: | G. Willems G. Pison P. J. Rousseeuw S. Van Aelst |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of Antwerp (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium., BE |
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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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