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Testing for a finite mixture model with two components


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  • Hanfeng Chen
  • Jiahua Chen
  • John D. Kalbfleisch
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    We consider a finite mixture model with "k" components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis "k"=2 "versus""k"⩾3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the support points are consistent. The asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied. Simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal, binomial and Poisson kernels suggest that the test proposed performs well. Simulation studies are also conducted for a bootstrap method with normal kernels. An example involving foetal movement data from a medical study illustrates the testing procedure. Copyright 2004 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

    Volume (Year): 66 (2004)
    Issue (Month): 1 ()
    Pages: 95-115

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    Handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:95-115

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    Cited by:
    1. María Gallegos & Gunter Ritter, 2009. "Trimming algorithms for clustering contaminated grouped data and their robustness," Advances in Data Analysis and Classification, Springer, vol. 3(2), pages 135-167, September.
    2. Dannemann, Jörn & Holzmann, Hajo, 2010. "Testing for two components in a switching regression model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1592-1604, June.
    3. Zhu, Hongtu & Zhang, Heping, 2006. "Asymptotics for estimation and testing procedures under loss of identifiability," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 19-45, January.
    4. Hajo Holzmann & Sebastian Vollmer & Julian Weisbrod, 2007. "Twin Peaks or Three Components? - Analyzing the World\'s Cross-Country Distribution of Income," Ibero America Institute for Econ. Research (IAI) Discussion Papers 162, Ibero-America Institute for Economic Research.
    5. Sebastian Vollmer & Hajo Holzmann & Florian Schwaiger, 2013. "Peak vs Components," Review of Development Economics, Wiley Blackwell, vol. 17(2), pages 352-364, 05.
    6. Lu, Zeng-Hua, 2009. "Covariate selection in mixture models with the censored response variable," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2710-2723, May.
    7. Kerby Shedden & Robert Zucker, 2008. "Regularized Finite Mixture Models for Probability Trajectories," Psychometrika, Springer, vol. 73(4), pages 625-646, December.
    8. Vadim Marmer, 2008. "Testing the null hypothesis of no regime switching with an application to GDP growth rates," Empirical Economics, Springer, vol. 35(1), pages 101-122, August.
    9. Cui, Yin & Fu, Yuejiao & Hussein, Abdulkadir, 2009. "Group sequential testing of homogeneity in genetic linkage analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3630-3639, August.
    10. Pittau, Maria Grazia & Zelli, Roberto & Johnson, Paul, . "Mixture Models and Convergence Clubs," Vassar College Department of Economics Working Paper Series 91, Vassar College Department of Economics.
    11. Andrew Sweeting, 2008. "The Strategic Timing Incentives of Commercial Radio Stations: An Empirical Analysis Using Multiple Equilibria," NBER Working Papers 14506, National Bureau of Economic Research, Inc.
    12. Gallegos, María Teresa & Ritter, Gunter, 2010. "Using combinatorial optimization in model-based trimmed clustering with cardinality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 637-654, March.
    13. Christian Ritz, 2013. "Penalized likelihood ratio tests for repeated measurement models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 534-547, September.


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