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Generalized p-values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA

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  • Gamage, Jinadasa
  • Mathew, Thomas
  • Weerahandi, Samaradasa

Abstract

For two multivariate normal populations with unequal covariance matrices, a procedure is developed for testing the equality of the mean vectors based on the concept of generalized p-values. The generalized p-values we have developed are functions of the sufficient statistics. The computation of the generalized p-values is discussed and illustrated with an example. Numerical results show that one of our generalized p-value test has a type I error probability not exceeding the nominal level. A formula involving only a finite number of chi-square random variables is provided for computing this generalized p-value. The formula is useful in a Bayesian solution as well. The problem of constructing a confidence region for the difference between the mean vectors is also addressed using the concept of generalized confidence regions. Finally, using the generalized p-value approach, a solution is developed for the heteroscedastic MANOVA problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:177-189
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Roy, Anindya & Bose, Arup, 2009. "Coverage of generalized confidence intervals," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1384-1397, August.
    2. Mar Fenoy & Pilar Ibarrola & Juan B. Seoane-Sepúlveda, 2019. "Generalized p value for multivariate Gaussian stochastic processes in continuous time," Statistical Papers, Springer, vol. 60(6), pages 2013-2030, December.
    3. Lajos Horváth & Gregory Rice, 2015. "Testing Equality Of Means When The Observations Are From Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 84-108, January.
    4. S.H. Lin, 2014. "Comparing the mean vectors of two independent multivariate log-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 259-274, February.
    5. Rendao Ye & Tiefeng Ma & Songgui Wang, 2011. "Generalized confidence intervals for the process capability indices in general random effect model with balanced data," Statistical Papers, Springer, vol. 52(1), pages 153-169, February.
    6. Jin-Ting Zhang & Xuefeng Liu, 2013. "A modified Bartlett test for heteroscedastic one-way MANOVA," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 135-152, January.
    7. 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.
    8. Tang, Shijie & Tsui, Kam-Wah, 2007. "Distributional properties for the generalized p-value for the Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 1-8, January.
    9. Girón, Fco. Javier & del Castillo, Carmen, 2010. "The multivariate Behrens-Fisher distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2091-2102, October.
    10. Xu, Li-Wen, 2015. "Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 291-303.
    11. Xu, Li-Wen & Wang, Song-Gui, 2008. "A new generalized p-value for ANOVA under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 963-969, June.
    12. Bebu, Ionut & Luta, George & Mathew, Thomas & Kennedy, Paul A. & Agan, Brian K., 2016. "Parametric cost-effectiveness inference with skewed data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 210-220.
    13. Lai, Chin-Ying & Tian, Lili & Schisterman, Enrique F., 2012. "Exact confidence interval estimation for the Youden index and its corresponding optimal cut-point," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1103-1114.

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