Affiliations: [a] Department of Informatics and Computer Science, Faculty of Sciences and Health Technology, Kalasin University, Nuea, Thailand | [b] Department of Science and Mathematics, Faculty of Sciences, Kalasin University, Nuea, Thailand
Correspondence:
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Corresponding author: Noppakun Thongmual, Faculty of Sciences, Department of Science and Mathematics, Kalasin University, 46000, Thailand. E-mail: [email protected].
Abstract: This article presents a comparison of multivariate normal mean vectors under covariance positive definite matrices. We introduce an improved parametric bootstrap (IPB) approach for addressing the multivariate Behrens-Fisher problem, specifically focusing on cases with unequal covariance matrices. Additionally, we evaluate the performance of the IPB test by comparing it with three existing tests: the parametric bootstrap (PB) test, the generalized variable (GV) test, and the Johansen test. Through Monte Carlo simulation, our results demonstrate that both the IPB test and the PB test exhibit superior control over Type I error rates compared to the GV and Johansen tests. Notably, the IPB test outperforms the PB test in terms of controlling Type I error rates. Consequently, our study concludes that the IPB test represents a preferred statistical method for testing the equality of mean vectors in the multivariate Behrens-Fisher problem.
Keywords: Parametric bootstrap, Type I error rates, Behrens-Fisher problem, unequal covariance
