Robust modified classical spherical tests in the presence of outliers

Abstract

This paper verifies if the classical test to sphericity hypotheses with homogeneous variances equal to one and null covariances is applicable for cases in the presence of outliers based on four different tests performed to verify its robustness. The classical likelihood ratio test (LTR) is applied and we also propose some of its modifications in wich the sample covariance matrix is switched by one of its robust estimators, and since there is an assumption violation due to the presence of outliers, a Monte Carlo version of both asymptotic versions is considered. The normal and contaminated normal distributions are also considered. In conclusion, two of the tests are robust in the presence of outliers in a multivariate normal distribution: the Monte Carlo version of the original test (LRTMC) and the Monte Carlo version of the modified test where the sample covariance matrix is switched by the comedian estimator (LRTMCR), and the most powerful test is LRTMC.