B1591
Title: $T^2$ type test statistic and simultaneous confidence intervals for sub-mean vectors in two-sample problem
Authors: Tamae Kawasaki - Aoyama Gakuin University (Japan) [presenting]
Takashi Seo - Tokyo University of Science (Japan)
Abstract: The test for sub-mean vectors in the two-sample problem is discussed. We consider testing the equality of the mean vectors of the two populations in the first $p_1$ dimensions (total dimension is $p_1+p_2$) under the assumption that the last $p_2$ dimensions in the mean vectors of the two populations are equal. The goal is to propose the $T^2$ type test statistic and the simultaneous confidence intervals for sub-mean vectors. In order to propose the $T^2$ type test statistic, we obtain the maximum likelihood estimators, and derive the asymptotic expansion of part of the test statistic for this case where the total sample size is large. We approximate the distribution for the $T^2$ type test statistics by constant times an $F$ distribution by adjusting the degrees of freedom. The simultaneous confidence intervals for all linear compounds of the difference of two sub-mean vectors are also given. Finally, the accuracy and asymptotic behavior of the approximation are investigated using 1,000,000 trials Monte Carlo simulation.