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Testing Homogeneity in Gamma Mixture Models

Author

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  • XIN LIU
  • CRISTIAN PASARICA
  • YONGZHAO SHAO

Abstract

This paper characterizes the asymptotic behaviour of the likelihood ratio test statistic (LRTS) for testing homogeneity (i.e. no mixture) against gamma mixture alternatives. Under the null hypothesis, the LRTS is shown to be asymptotically equivalent to the square of Davies's Gaussian process test statistic and diverges at a log n rate to infinity in probability. Based on the asymptotic analysis, we propose and demonstrate a computationally efficient method to simulate the null distributions of the LRTS for small to moderate sample sizes.

Suggested Citation

  • Xin Liu & Cristian Pasarica & Yongzhao Shao, 2003. "Testing Homogeneity in Gamma Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 227-239, March.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:1:p:227-239
    DOI: 10.1111/1467-9469.00328
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    Citations

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    Cited by:

    1. Mingxing He & Jiahua Chen, 2022. "Strong consistency of the MLE under two-parameter Gamma mixture models with a structural scale parameter," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 125-154, March.
    2. Fitzpatrick, Matthew & Stewart, Michael, 2022. "Asymptotics for Markov chain mixture detection," Econometrics and Statistics, Elsevier, vol. 22(C), pages 56-66.
    3. Garel, Bernard, 2007. "Recent asymptotic results in testing for mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5295-5304, July.
    4. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    5. Chen, Qikun & Stewart, Michael, 2024. "Optimal detection of sparse gamma scale admixture with twice the null mean," Statistics & Probability Letters, Elsevier, vol. 209(C).
    6. 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.
    7. Jin Seo Cho & Jin Seok Park & Sang Woo Park, 2018. "Testing for the Conditional Geometric Mixture Distribution," Working papers 2018rwp-123, Yonsei University, Yonsei Economics Research Institute.
    8. Mingxing He & Jiahua Chen, 2022. "Consistency of the MLE under a two-parameter Gamma mixture model with a structural shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 951-975, November.
    9. Hung-Chia Chen & James J. Chen, 2016. "Hybrid Mixture Model for Subpopulation Identification," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(1), pages 28-42, June.

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