TY - JOUR
AU - SILVA, Vanessa Siqueira Peres da
AU - FERREIRA, Daniel Furtado
PY - 2016/06/28
Y2 - 2022/08/11
TI - NONPARAMETRIC BOOTSTRAP TEST FOR EQUAL COVARIANCE MATRICES OF TWO DEPENDENT MULTIVARIATE NORMAL POPULATIONS
JF - Brazilian Journal of Biometrics
JA - Braz. J. Biom.
VL - 34
IS - 2
SE - Articles
DO -
UR - https://biometria.ufla.br/index.php/BBJ/article/view/137
SP - 210-232
AB - <p>This study aims to evaluate the type I error rates and power of the nonparametric bootstrap test (t<sub>b0</sub>) 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) (W<sub>2</sub> and W<sub>5</sub>) and Jiang et al. (1999) (LRT, LRT<sub>1</sub>, LRT<sub>2</sub> and LRT<sub>3</sub>). For this simulations Monte Carlo were performed, considering the number of variables (<em>p</em>), sample sizes (<em>n</em>), covariance matrices (Σ) and signicance level (α) of 0.05. In the first case, for <em>p</em> = 2, it was concluded that among the tests that controlled the type I error, the tests t<sub>b0</sub> , LRT<sub>3</sub> and W<sub>2</sub> were greater than its competitors in all cases studied. In relation to power, the test t<sub>b0</sub> approached the testing LRT<sub>3</sub> and W<sub>2</sub> and is considered intermediate. In the second case, it is considered that <em>p</em> = 4 and <em>p</em> = 10, it was concluded that the test tb0 showed high performance, in most cases equal to 100% even for small samples (<em>n</em> = 20). Therefore, we recommend the application of the proposed test tb0 in real situations.</p>
ER -