Robust testing based on density power divergence for comparing multiple means in the ANCOVA model

Abstract

This paper introduces a robust approach to the analysis of covariance (ANCOVA) method, which addresses the challenges posed by outliers and violations of assumptions. ANCOVA is commonly employed to assess the equality of multiple means across different factor levels while accounting for the influence of concomitant variables on the response. However, the traditional ANCOVA test can yield unreliable outcomes when faced with such challenges, leading to an increased likelihood of false positive and false negative results. To overcome these issues, we propose a robust ANCOVA test utilizing an M-estimator framework based on the minimum density power divergence estimator (MDPDE). The robustness and asymptotic properties of the proposed test are rigorously established under mild regularity conditions. Furthermore, through an extensive simulation study and the analysis of two empirical datasets (the prostate cancer dataset and the barley dataset), we demonstrate the superior performance of our proposed test in the presence of data contamination, outperforming both classical ANCOVA and other existing robust tests.