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Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models

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  • Wong, Tony S.T.
  • Lam, Kwok Fai
  • Zhao, Victoria X.

Abstract

Likelihood-based methods play a central role in statistical inference for parametric models. Among these, the modified likelihood ratio test is preferred in testing for homogeneity in finite mixture models. The test statistic is related to the maximum of a quadratic function under general regularity conditions. Re-parameterization is shown to have overcome the difficulty when linear independence is not satisfied. Models with parameter constraints are also considered. The asymptotic null distribution of the test statistic is shown to have a chi-bar-squared distribution in both constrained and unconstrained cases. We extend the result to linear models and demonstrate that the chi-bar-squared distribution is also applicable. The general asymptotic result provides a much simpler testing procedure with an exact form of the asymptotic distribution compared to re-sampling approach in the literature. It also offers accurate p-value as shown in simulation. The results are checked by extensive simulation and are supplemented by a breast cancer data example.

Suggested Citation

  • Wong, Tony S.T. & Lam, Kwok Fai & Zhao, Victoria X., 2018. "Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 248-257.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:248-257
    DOI: 10.1016/j.csda.2018.05.010
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    References listed on IDEAS

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    1. Shaoting Li & Jiahua Chen & Jianhua Guo & Bing-Yi Jing & Shui-Ying Tsang & Hong Xue, 2015. "Likelihood Ratio Test for Multi-Sample Mixture Model and Its Application to Genetic Imprinting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 867-877, June.
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