NONPARAMETRIC BOOTSTRAP TEST FOR EQUAL COVARIANCE MATRICES OF TWO DEPENDENT MULTIVARIATE NORMAL POPULATIONS - SILVA, Vanessa Siqueira Peres da; FERREIRA, Daniel Furtado (Brazilian Journal of Biometrics, 2016)
This study aims to evaluate the type I error rates and power of the nonparametric bootstrap test (tb0) for equality of covariance matrices of two dependent multivariate normal populations in order to compare its performance with the test presented by Jiang and Sarkar (1998) (W2 and W5) and Jiang et al. (1999) (LRT, LRT1, LRT2 and LRT3). For this simulations Monte Carlo were performed, considering the number of variables (p), sample sizes (n), covariance matrices (Σ) and signicance level (α) of 0.05. In the first case, for p = 2, it was concluded that among the tests that controlled the type I error, the tests tb0 , LRT3 and W2 were greater than its competitors in all cases studied. In relation to power, the test tb0 approached the testing LRT3 and W2 and is considered intermediate. In the second case, it is considered that p = 4 and p = 10, it was concluded that the test tb0 showed high performance, in most cases equal to 100% even for small samples (n = 20). Therefore, we recommend the application of the proposed test tb0 in real situations.