A Comparing Robust Wilks’ statistics in Multivariate Multiple Linear Regression

Abstract

In multivariate linear regression, the classical Wilks’ statistic is the most used method to test hypotheses, which is extremely responsive to the effect of outliers. Many authors have examined the non-robust test statistic established on normal theories for various cases. In this study, we constructed a robust version of Wilks’ statistic relying on a reweighed minimum covariance determinant estimator, that relies on the weight of the observations, with the weights being determined by using the Hampel weight function and Huber weight function. A comparison of the suggested statistics with the regular Wilks’ statistic has been discussed. Monte Carlo studies are used to evaluate how well test statistics work with different datasets. So, this study looked at how two different test statistics perform under a normal distribution. The first is the classical Wilks’ statistic, and the second is a proposed new one. For both of them, the rate of type I errors and the power of the tests were close to the expected significance levels. In situations where the distribution is contaminated, the proposed statistical method works best. If the data has been corrupted or affected somehow, this approach seems to perform the best out of the options

Keywords

• Minimum Covariance Determinant Estimator
• Outliers
• Robustness
• P-Value
• Wilk's Statistic