Abstract | ||
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In this paper, we consider testing the equality of two mean vectors with unequal covariance matrices. In the case of equal covariance matrices, we can use Hotelling's T-2 statistic, which follows the F distribution under the null hypothesis. Meanwhile, in the case of unequal covariance matrices, the T-2 type test statistic does not follow the F distribution, and it is also difficult to derive the exact distribution. In this paper, we propose an approximate solution to the problem by adjusting the degrees of freedom of the F distribution. Asymptotic expansions up to the term of order N-2 for the first and second moments of the U statistic are given, where N is the total sample size minus two. A new approximate degrees of freedom and its bias correction are obtained. Finally, numerical comparison is presented by a Monte Carlo simulation. |
Year | DOI | Venue |
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2015 | 10.1080/03610918.2013.824587 | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION |
Keywords | DocType | Volume |
Approximate degrees of freedom,Bias correction,F approximation,Hotelling's T-2 statistic,Multivariate Behrens-Fisher problem,Two sample problem | Journal | 44 |
Issue | ISSN | Citations |
7 | 0361-0918 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
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Tamae Kawasaki | 1 | 0 | 0.34 |
Takashi Seo | 2 | 0 | 3.04 |