Journal of Statistics Applications & Probability


The classical Wilks’ statistic is mostly used to test hypotheses in the one-way multivariate analysis of variance (MANOVA), which is highly sensitive to the effects of outliers. The non-robustness of the test statistics based on normal theory has led many authors to examine various options. In 2010, Todorov and Filzmoser proposed a robust Wilks’ statistic depends on reweighted minimum covariance determinant estimator (RMCD) and constructed its approximate distribution. In this paper, we presented a robust version of the Wilks’ statistics based on reweighted minimum covariance determinant estimator and reweighted minimum volume ellipsoid estimator, and constructed it’s another approximate distribution depends on the weights of observations, where the weights are calculated based on Hampel weight function. A comparison was made between the proposed statistics, classical Wilks’ statistic, and the robust Wilks’ statistic which is proposed by Todorov and Filzmoser. The Monte Carlo studies are used to obtain performance assessment of test statistics in different data sets. Moreover, the results of the type I error rate and the power of test were considered as statistical tools to compare test statistics. The study reveals that, under normally distributed, the type I error rates for the classical and the proposed Wilks’ statistics are close to the true significance levels, and the power of the test statistics are so close. In addition, in the case of contaminated distribution, the proposed statistics is the best. A real data are used to further evaluate the proposed robust statistics in this study.

Digital Object Identifier (DOI)