IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i4p1177-1190.html
   My bibliography  Save this article

Generalized F-tests for the multivariate normal mean

Author

Listed:
  • Liang, Jiajuan
  • Tang, Man-Lai

Abstract

Based on Läuter's [Läuter, J., 1996. Exact t and F tests for analyzing studies with multiple endpoints. Biometrics 52, 964-970] exact t test for biometrical studies related to the multivariate normal mean, we develop a generalized F-test for the multivariate normal mean and extend it to multiple comparison. The proposed generalized F-tests have simple approximate null distributions. A Monte Carlo study and two real examples show that the generalized F-test is at least as good as the optional individual Läuter's test and can improve its performance in some situations where the projection directions for the Läuter's test may not be suitably chosen. The generalized F-test could be superior to individual Läuter's tests and the classical Hotelling T2-test for the general purpose of testing the multivariate normal mean. It is shown by Monte Carlo studies that the extended generalized F-test outperforms the commonly-used classical test for multiple comparison of normal means in the case of high dimension with small sample sizes.

Suggested Citation

  • Liang, Jiajuan & Tang, Man-Lai, 2009. "Generalized F-tests for the multivariate normal mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1177-1190, February.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1177-1190
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00488-X
    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. Glimm, Ekkehard & Läuter, Jürgen, 2003. "On the admissibility of stable spherical multivariate tests," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 254-265, August.
    2. Fang, Kai-Tai & Li, Run-Ze & Liang, Jia-Juan, 1998. "A multivariate version of Ghosh's T3-plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 371-386, October.
    3. Tan, Ming & Fang, Hong-Bin & Tian, Guo-Liang & Wei, Gang, 2005. "Testing multivariate normality in incomplete data of small sample size," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 164-179, March.
    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. Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    2. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.

    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. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    2. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    3. Liang, Jia-Juan & Bentler, Peter M., 1999. "A t-distribution plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 31-44, March.
    4. Simos G. Meintanis & Zdeněk Hlávka, 2010. "Goodness‐of‐Fit Tests for Bivariate and Multivariate Skew‐Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 701-714, December.
    5. Liang, Jiajuan & Pan, William S.Y. & Yang, Zhen-Hai, 2004. "Characterization-based Q-Q plots for testing multinormality," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 183-190, December.
    6. Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    7. Daniel McNeish, 2017. "Missing data methods for arbitrary missingness with small samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 24-39, January.
    8. Nieto-Reyes, Alicia & Cuesta-Albertos, Juan Antonio & Gamboa, Fabrice, 2014. "A random-projection based test of Gaussianity for stationary processes," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

    More about this item

    Statistics

    Access and download statistics

    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:csdana:v:53:y:2009:i:4:p:1177-1190. 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/locate/csda .

    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.