IDEAS home Printed from
   My bibliography  Save this article

A moment-based test for the homogeneity in mixture natural exponential family with quadratic variance functions


  • Ning, Wei
  • Zhang, Sanguo
  • Yu, Chang


In this paper, we propose a simple moment-based procedure for testing homogeneity in the natural exponential family with quadratic variance functions. In the literature, solutions to this problem normally involve establishing identifiability of parameters first, then testing the hypotheses whether the data come from a single distribution or a mixture of distributions. Our procedure directly tests the hypotheses without the need to establish parameter estimability. Simulation studies demonstrate that the power of our test is comparable to the supplementary score test and the separate score test proposed by Wu and Gupta [Wu, Y., Gupta, A.K., 2003. Local score tests in mixture exponential family. J. Statist. Plann. Inference 116, 421-435], and the normalized score test proposed by Shoukri and Lathrop [Shoukri, M., Lathrop, G.M., 1993. Statistical testing of genetic linkage under heterogeneity. Biometrics 49, 151-161]. In these simulation studies, the methods by the others are specific to cases with a known null distribution, and our methods can also be applied to cases with unknown null distribution. Our test procedure is demonstrated on two real data sets.

Suggested Citation

  • Ning, Wei & Zhang, Sanguo & Yu, Chang, 2009. "A moment-based test for the homogeneity in mixture natural exponential family with quadratic variance functions," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 828-834, March.
  • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:828-834

    Download full text from publisher

    File URL:
    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

    1. Lemdani, Mohamed & Pons, Odile, 1997. "Likelihood ratio tests for genetic linkage," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 15-22, April.
    2. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2001. "A modified likelihood ratio test for homogeneity in finite mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 19-29.
    3. Wu, Yanhong & Xu, Yongxia, 2000. "Local likelihood ratio tests in the normal mixture model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 323-329, December.
    4. Song Qin, Yong & Smith, Bruce, 2006. "The likelihood ratio test for homogeneity in bivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 474-491, February.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:stapro:v:79:y:2009:i:6:p:828-834. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.