A two-sample multivariate test with one covariance matrix unknown

Abstract

In this paper, we considered two-sample multivariate testing for testing the equality of two population mean vectors of two normal populations in this situation in which one covariance is assumed to be known and the other unknown when both the sample sizes are larger than their dimensions. We adapted a test statistic from Yao (1965) and developed its distribution. The accuracy of the proposed test is investigated by simulation study. Under simulation study, the simulated results showed that the attained significance levels of proposed tests are close to nominal significance level setting in every situation considered. All proposed tests gave excellent performance and power in every situation considered except when the sample size from population with known covariance matrix is smaller than that from population with unknown covariance matrix. The two-sided proposed test and the one-sided proposed test as Ha: μ1 < μ2 work very well when the dimension is less than 30. Finally, we applied the proposed tests for analyzing the real data.

Keywords

• approximate degrees of freedom
• covariance matrix unknown
• hypothesis testing
• multivariate behrens–fisher problem
• two–sample multivariate test