Estudo de desempenho de testes de hipóteses multivariados no caso de dados de duas populações independentes

Abstract

Hypothesis tests are widely used in various fields.There are situations where several variables are measured on same elements of the population and the hypothesis of interest involves a parameter vector of the joint probability distribution of these variables. The well-known Hotellings T2 multivariate hypothesis testing is used to test the population mean vector for one or two populations. An alternative test was proposed by Hayter and Tsui in 1994, only for the case of one population. Thus, the main objective of this dissertation is to extent Hayter and Tsuis test for the comparison of the mean vectors of two independent populations. Three new tests which are combinations of the Hotellings T2 and Hayter and Tsui tests are proposed in an attempt to obtain a test more powerful than the tests individually, taking the advantage of the quality of these two tests. The performance of the proposed tests were evaluated by Monte Carlo simulation, and all of them compared to the usual Hotellings T2, regarding the power of the tests. The proposed extension of Hayter and Tsui test proved to be comparable to the usual Hotellings T2 test, reaching higher power values in some cases. The tests of combination of p-values by Tippett (1931) and Fisher (1950) also proved to be effective, also exceeding the power values of T2 Hotelling and Hayter and Tsuis tests in some simulated scenarios.