Robust Wilks' Statistic based on RMCD for One-Way Multivariate Analysis of Variance (MANOVA)

Abstract

The classical Wilks' statistic is the most using for testing the hypotheses of equal mean vectors of several multivariate normal populations for one-way MANOVA. It is extremely sensitive to the influence of outliers. Therefore, the robust Wilks' statistic based on reweighted minimum covariance determinant (RMCD) estimator with Hampel weighted function has been proposed. The distribution of the proposed statistic differs from the classical one.

Mont Carlo simulations are used to evaluate the performance of the test statistic under the normal and contaminated distribution for the data set. Moreover, the type I error rate and power of test have been considered as statistical measures to comparison between the classical and the robust statistics.

The results show that, the robust Wilks' statistic based on RMCD is closely to the classical Wilks' statistic in case of normal distribution for the data set while in case of contaminated distribution the method in question is the best.

Keywords: One-Way Multivariate Analysis of Variance, Wilks' Statistic, Outliers, Robustness, Minimum Covariance Determinant Estimator.