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Inferences on a linear combination of K multivariate normal mean vectors

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  • S. H. Lin
  • R. S. Wang

Abstract

In this paper, the hypothesis testing and confidence region construction for a linear combination of mean vectors for K independent multivariate normal populations are considered. A new generalized pivotal quantity and a new generalized test variable are derived based on the concepts of generalized p-values and generalized confidence regions. When only two populations are considered, our results are equivalent to those proposed by Gamage et al. [Generalized p-values and confidence regions for the multivariate Behrens-Fisher problem and MANOVA, J. Multivariate Aanal. 88 (2004), pp. 117-189] in the bivariate case, which is also known as the bivariate Behrens-Fisher problem. However, in some higher dimension cases, these two results are quite different. The generalized confidence region is illustrated with two numerical examples and the merits of the proposed method are numerically compared with those of the existing methods with respect to their expected areas, coverage probabilities under different scenarios.

Suggested Citation

  • S. H. Lin & R. S. Wang, 2009. "Inferences on a linear combination of K multivariate normal mean vectors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(4), pages 415-428.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:4:p:415-428
    DOI: 10.1080/02664760802474231
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    References listed on IDEAS

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    1. Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2004. "Generalized p-values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 177-189, January.
    2. Thursby, Jerry G., 1992. "A comparison of several exact and approximate tests for structural shift under heteroscedasticity," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 363-386.
    3. Krishnamoorthy, K. & Yu, Jianqi, 2004. "Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 161-169, January.
    4. Jenö Reiczigel, 1999. "Analysis of Experimental Data with Repeated Measurements," Biometrics, The International Biometric Society, vol. 55(4), pages 1059-1063, December.
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