Compare Robust Wilk’s statistics Based on MM-estimator for the Multivariate Multiple Linear Regression

Abstract

 In the realm of multivariate linear regression, the classical Wilks' statistic stands out as a widely employed method for hypothesis testing, yet it exhibits high sensitivity to the influence of outliers. Numerous authors have explored non-robust test statistics grounded in normal theories across diverse scenarios. In this investigation, we developed a robust variant of the Wilks' statistics, utilizing the MM-estimator. This approach relies on observation weights determined through Hampel and Huber weight functions. We conducted a comparative analysis between the proposed statistics and the conventional Wilks' statistic. Monte Carlo studies were employed to assess the performance of the test statistics across various datasets, particularly under normal distribution conditions. The study delves into the comparative effectiveness of two test statistics—classical Wilks' and the newly proposed robust statistics. Both exhibited type I error rates and test power close to expected significance levels. However, in scenarios involving data contamination, the proposed statistical method demonstrated superior performance. It emerged as the preferred approach when dealing with corrupted or affected data.