A Robust Hotelling Test

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.