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A Robust Hotelling Test

In: Developments in Robust Statistics

Author

Listed:
  • G. Willems

    (University of Antwerp (UIA), Department of Mathematics and Computer Science)

  • G. Pison

    (University of Antwerp (UIA), Department of Mathematics and Computer Science)

  • P. J. Rousseeuw

    (University of Antwerp (UIA), Department of Mathematics and Computer Science)

  • S. Van Aelst

    (University of Antwerp (UIA), Department of Mathematics and Computer Science)

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.

Suggested Citation

  • G. Willems & G. Pison & P. J. Rousseeuw & S. Van Aelst, 2003. "A Robust Hotelling Test," Springer Books, in: Rudolf Dutter & Peter Filzmoser & Ursula Gather & Peter J. Rousseeuw (ed.), Developments in Robust Statistics, pages 417-431, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57338-5_36
    DOI: 10.1007/978-3-642-57338-5_36
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