IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v88y2004i1p177-189.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00065-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Girón, Fco. Javier & del Castillo, Carmen, 2010. "The multivariate Behrens-Fisher distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2091-2102, October.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Joachim Zietz, 2006. "Detecting neglected parameter heterogeneity with Chow tests," Applied Economics Letters, Taylor & Francis Journals, vol. 13(6), pages 369-374.
    3. Maasoumi, Esfandiar & Zaman, Asad & Ahmed, Mumtaz, 2010. "Tests for structural change, aggregation, and homogeneity," Economic Modelling, Elsevier, vol. 27(6), pages 1382-1391, November.
    4. Lin, Shu-Hui & Lee, Jack C., 2003. "Exact tests in simple growth curve models and one-way ANOVA with equicorrelation error structure," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 351-368, February.
    5. Boyd Hunter, 1996. "Explaining Changes in the Social Structure of Employment: The Importance of Geography," Discussion Papers 0067, University of New South Wales, Social Policy Research Centre.
    6. Ho, Yu-Yun & Weerahandi, Sam, 2007. "Analysis of repeated measures under unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 493-504, March.
    7. Pedro Bação, 2006. "The Performance of Structural Change Tests," Quality & Quantity: International Journal of Methodology, Springer, vol. 40(4), pages 611-628, August.
    8. Gebrenegus Ghilagaber, 2004. "Another Look at Chow's Test for the Equality of Two Heteroscedastic Regression Models," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(1), pages 81-93, February.
    9. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5.
    10. Samaradasa Weerahandi & Vance W. Berger, 1999. "Exact Inference for Growth Curves with Intraclass Correlation Structure," Biometrics, The International Biometric Society, vol. 55(3), pages 921-924, September.
    11. E. Dijkgraaf & R. Gradus, 2003. "Cost Savings of Contracting Out Refuse Collection," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 30(2), pages 149-161, June.
    12. Masafumi Akahira, 2002. "Confidence intervals for the difference of means: application to the Behrens-Fisher type problem," Statistical Papers, Springer, vol. 43(2), pages 273-284, April.
    13. Joachim Zietz & Bobby Newsome, 2002. "Agency Representation and the Sale Price of Houses," Journal of Real Estate Research, American Real Estate Society, vol. 24(2), pages 165-192.
    14. David Brasington, 2002. "Differences in the Production of Education Across Regions and Urban and Rural Areas," Regional Studies, Taylor & Francis Journals, vol. 36(2), pages 137-145.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:177-189. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.