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The likelihood ratio test for homogeneity in bivariate normal mixtures

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  • Song Qin, Yong
  • Smith, Bruce

Abstract

This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in a bivariate normal mixture model with known covariance. The asymptotic null distributions of the likelihood ratio statistic and a modified likelihood ratio statistic are obtained in explicit form. The distributions are identical. The results of a small simulation study to approximate the null distribution are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:474-491
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    References listed on IDEAS

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    1. 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.
    2. Chen, Hanfeng & Chen, Jiahua, 2001. "Large sample distribution of the likelihood ratio test for normal mixtures," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 125-133, April.
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    Cited by:

    1. Wong, Tony Siu Tung & Li, Wai Keung, 2014. "Test for homogeneity in gamma mixture models using likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 127-137.
    2. 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.

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