A Robust Hotelling Test

G. Willems (), G. Pison (), Peter Rousseeuw and S. Van Aelst
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G. Willems: University of Antwerp (UIA), Department of Mathematics and Computer Science
G. Pison: University of Antwerp (UIA), Department of Mathematics and Computer Science
S. Van Aelst: University of Antwerp (UIA), Department of Mathematics and Computer Science

A chapter in Developments in Robust Statistics, 2003, pp 417-431 from Springer

Abstract: Summary Hotelling’s T2 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 (Rousseeuw, 1984) instead of the classical mean and covariance matrix. Recently, a fast algorithm was constructed to compute the MCD (Rousseeuw and Van Driessen, 1999). 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 T2 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 T2 are investigated through simulation.

Keywords: Monte Carlo Study; Approximate Distribution; Minimum Covariance Determinant; Simultaneous Confidence Interval; Robust Distance (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57338-5_36

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DOI: 10.1007/978-3-642-57338-5_36

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