Proposal of multivariate multiple comparison tests with the control treatment - Costa Braz, Lúcia Helena; Carvalho Nascimento, Miguel; Furtado Ferreira, Daniel (Brazilian Journal of Biometrics, 2026)
Problems involving comparisons of treatment effectiveness for multivariate responses are common in various fields of knowledge. Typically, methods for comparing vectors of means use the Bonferroni inequality to construct conservative tests, avoiding the complexities of the exact distribution of the maximum test statistic T2 max, the maximum of Hotelling’s T2. In high-dimensional scenarios, traditional methods are not viable as they depend on the inverse of the sample covariance matrix, which becomes singular. To address this problem, Dempster’s trace criterion can be used, and a second alternative is Ahmad’s test statistic Tig, however, in both cases, the Bonferroni inequality is used. Another issue is that both in the estimation process and in the exact distribution of statistics for multiple comparison tests, there is a need to deal with sophisticated and complex numerical methods. These facts make these approximations not readily usable. To try to overcome these challenges, this work proposes multivariate multiple comparison tests with the control treatment using the nonparametric bootstrap method. The performance of the tests was evaluated through experimentwise type I error rates (EER) and power in different scenarios using Monte Carlo simulation and the R program. The results showed that for homoscedastic scenarios, the proposed bootstrap test ATB showed more effective control of EER, in addition to having higher power, regardless of whether the distribution was normal or not, in both low and high-dimensional contexts. Thus, the ATB test proved to be the most recommended alternative in these situations. For heteroscedastic scenarios, it was not possible to identify a clearly superior test, but in several circumstances, the proposed bootstrap tests demonstrated superior performance compared to their respective asymptotic versions.