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

• Ano de defesa: 2023
• Autor(a) principal: Campos, Laíla Luana
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Lavras; Programa de Pós-graduação em Estatística e Experimentação Agropecuária; UFLA; brasil; Departamento de Estatística
• Palavras-chave em Português: Robustez; Matriz de covariância; Simulação Monte Carlo; Bootstrap; Robustness; Covariance matrix; Monte Carlo simulation; Regressão e Correlação
• Link de acesso: http://repositorio.ufla.br/jspui/handle/1/56389

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.