Proposta de testes de esfericidade robustos quanto a presença de outliers e a alta dimensionalidade dos dados

Abstract

For the sphericity hypothesis, the study of ten tests was proposed to verify the robustness regarding the presence of outliers and the high dimensionality of the data. As the likelihood ratio test degenerates when p ≥ n, the test statistic proposed by John (1971) was applied, as it is robust when p ≥ n, and its modifications, in which the covariance matrix was replaced by its robust comedian estimator (JAsR), its bootstrap version (JB) and the modification of the bootstrap version, which replaced the sample covariance matrix by its robust comedian estimator (JBR) . The likelihood ratio test (LRTAs) was also studied, as well as the LRTAs with modified test statistics, following the same criteria as the J statistic: LRTAsR, LRTB and LRTBR. An adaptation of the maximum test statistic proposed by Chen et al. (2020) was also used: TB and TBR. The normal and contaminated normal distributions with 30% contamination were used. It was concluded that the bootstrap versions of the tests performed better, as they were robust in terms of the presence of outliers, and that JB and JBR were also robust in relation to the high dimensionality of the data.