A robust hotelling testA robust hotelling test
Faculty of Sciences. Mathematics and Computer Science

Faculty of Social Sciences. Communication Sciences

Statistics and data analysis

Visual and Digital Cultures Research Center (ViDi)

Department of Mathematics - Computer Sciences

conferenceObject

2003 2003

Mathematics

Developments in robust statistics

International Conference on Robust Statistics (ICOR 2001), JUL 23-27, 2001, VORAU, AUSTRIA

(2003), p. 417-431

3-7908-1518-7

000179943000036

E

English (eng)

University of Antwerp

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 (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 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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