T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors

Tamae Kawasaki, Toshiki Naito and Takashi Seo

International Journal of Statistics and Probability, 2020, vol. 9, issue 1, 1

Abstract: In this paper, we consider tests for sub-mean vectors and its simultaneous confidence intervals in two-sample problems. We give the T^2 type test statistic and the simultaneous confidence intervals by using two approximate upper percentiles of T^2 type test statistic. One of the approximate percentiles is obtained by normal approximation for a part of the T^2 type statistic, and the other is an approximation obtained by correcting the degrees of freedom of the F distribution. Finally, we investigate the asymptotic behavior of the approximate upper percentiles of T^2 type statistic by Monte Carlo simulation, and we give an example to illustrate the simultaneous confidence intervals.

Date: 2020
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