Proposição de testes de comparações múltiplas multivariadas com o tratamento controle

Abstract

Problems involving comparisons of treatment efficiency for multivariate responses are common in various fields of knowledge. Generally, comparison methods use the Bonferroni inequality to construct conservative tests, avoiding the complexities of the exact distribution of the T 2 max test statistic (maximum of a Hotelling’s T 2 ). In high-dimensional scenarios, traditional methods are not viable, as they depend on the inverse of the sample covariance matrix, which becomes singular. To circumvent this problem, Dempster’s trace criterion can be used, and a second alternative is Ahmad’s Tig test statistic; however, in both cases, the Bonferroni inequality is employed. Another issue is that both in the estimation process and in the distribution of the statistics for multiple comparison tests, it is necessary to deal with sophisticated and complex numerical methods. These facts make these approximations unsuitable for immediate use. To address these challenges, this thesis proposes multivariate multiple comparison tests with the control treatment, using an empirical approximation for the second-order Bonferroni approxi- mation and the non parametric bootstrap method. The performance of the tests was evaluated through type I error rates per experiment (TEE) and power in different scenarios, using Monte Carlo simulation and the R software. The results showed that, for homoscedastic scenarios, the proposed bootstrap test TAB provided more effective control of TEE, in addition to exhi- biting higher power, regardless of whether the distribution was normal or not, in both low and high-dimensional contexts. Thus, the TAB test proved to be the most recommended alternative in these situations. For heteroscedastic scenarios, no clearly superior test could be identified; however, in many circumstances, the proposed bootstrap tests demonstrated superior perfor- mance compared to their respective asymptotic versions.