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Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter

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Abstract

This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ 22 null limiting distribution.

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References

  1. Lindsay B G. Moment matrices: applications in mixtures. Ann Statist, 17: 722–740 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Leroux B. Consistent estimation of a mixture distribution. Ann Statist, 20: 1350–1360 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chernoff H, Lander E. Asymptotic distribution of the likelihood ratio test that a mixture of two binomials is a single binomial. J Statist Plann Inference, 43: 19–40 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cheng R C H, Traylor L. Non-regular maximum likelihood problems (with discussion). J R Statist Soc B, 57: 3–44 (1995)

    MATH  MathSciNet  Google Scholar 

  5. Chen H, Chen J. Large sample distribution of the likelihood ratio test for normal mixtures. Statist Probab Lett, 52: 125–133 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen H, Chen J. Tests for homogeneity in normal mixture with presence of a structural parameter. Statist Sinica, 13: 351–365 (2003)

    MATH  MathSciNet  Google Scholar 

  7. Chen H, Chen J, Kalbfleisch J D. A modified likelihood ratio test for homogeneity in finite mixture models. J R Statist Soc B, 63: 19–29 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  8. Qin Y, Smith B. Likelihood ratio test for homogeneity in normal mixtures in the presence of a structural parameter. Statist Sinica, 14: 1165–1177 (2004)

    MATH  MathSciNet  Google Scholar 

  9. Hartigan J A. A failure of likelihood asymptotics for normal mixtures. In: Lecam L, Olshen R A, eds. Proceedings of the Berkeley Conference in Honor of Neyman J and Kiefer J. Wadsworth: Belmont, 1985, 807–810

    Google Scholar 

  10. Chen H, Chen J, Kalbfleisch J D. A modified likelihood ratio test for homogeneity in the finite mixture models. Technical Report STAT 2000-01. Waterloo: Department of Statistics and Actuarial Science, University of Waterloo, 2000

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Guangxi Normal University, Guilin, 541004, China

    YongSong Qin & QingZhu Lei

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  1. YongSong Qin
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  2. QingZhu Lei
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Corresponding author

Correspondence to QingZhu Lei.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10661003), the Natural Science Foundation of Guangxi (Grant No. 0728092) and SRF for ROCS, SEM (Grant No. [2004]527)

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Qin, Y., Lei, Q. Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter. Sci. China Ser. A-Math. 51, 1871–1882 (2008). https://doi.org/10.1007/s11425-007-0180-7

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  • DOI: https://doi.org/10.1007/s11425-007-0180-7

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