Robust and Efficient One-Way MANOVA Tests

We propose robust tests as alternatives to the classical Wilks' Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multisample multivariate S-estimators or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis. We show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples. We also investigate the power of the new tests, as well as their robustness against outliers. Finally, we illustrate the use of these robust test statistics on a real data example. Some additional results are provided as supplemental material.