Proposição e avaliação de testes para independência entre grupos de variáveis

Abstract

For testing the independence of two random vectors follows a p_dimensional normal distribution, the Wilks test (likelihood ratio test, LRT) is used. However, it performs badly in the presence of outliers, as its estimator, which is the sample covariance matrix, is influenced by outliers and is also affected by the non-normality of the data. Thus, robust statistics should be used, such as the robust comedian estimator of the covariance matrix. Another issue to consider is the replacement of the determinant of the covariance matrix by the trace. Based on this, in this thesis, seven new asymptotic and robust tests for independence between two groups of variables were proposed and evaluated, through adaptations made both in the LRT test and in the new tests proposed using the trace criterion, being that these tests are asymptotic and others were built based on the parametric bootstrap method with and without the comedian estimator for the covariance matrix. The performance of these tests was evaluated and compared to the corrected Wilks LTR test, considering small and also of high dimension, from normal multivariate distributions, contaminated and non-normal distributions, using Monte Carlo simulations. The type I error rats and power were computed in all Monte Carlo simulations by using the R software. The prejudiced results that the LRT test with the replacement of the covariance matrix by the estimator comedian did not control the type I error rates, the test using the trace criterion was effective. showed that the proposed test T and TR control type I error rates also for non-normal distributions outperforming the ordinary test and the tests using the bootstrap method were effective in all situations evaluated.