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A Note for Likelihood Ratio Methods for Testing the Homogeneity of a Three-Sample Problem with a Mixture Structure

Author

Listed:
  • Pengcheng Ren

    (Jiangsu Normal University)

  • Guanfu Liu

    (Shanghai University of International Business and Economics)

  • Xiaolong Pu

    (East China Normal University)

  • Xingyu Yan

    (Jiangsu Normal University)

Abstract

Recently, our paper entitled “Generalized fiducial methods for testing the homogeneity of a three-sample problem with a mixture structure” is published in Journal of Applied Statistics 50 (2023), pp. 1094–1114. In simulation studies of this paper, the likelihood ratio method is regarded as a comparison method with the generalized fiducial methods. However, the construction of the likelihood ratio method and its asymptotic theories were not provided. It is worth noting that under the null model, the proportion parameter disappears, and it is unidentifiable. Hence, the classic theory of the likelihood ratio method is not applicable to the testing problem we consider. In consideration of the advantages owned by the likelihood ratio method, it is necessary to separately to establish the likelihood ratio method and study its asymptotic theory. Therefore, we write this note to highlight this method.

Suggested Citation

  • Pengcheng Ren & Guanfu Liu & Xiaolong Pu & Xingyu Yan, 2025. "A Note for Likelihood Ratio Methods for Testing the Homogeneity of a Three-Sample Problem with a Mixture Structure," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(1), pages 114-133, February.
    • Handle: RePEc:spr:sankha:v:87:y:2025:i:1:d:10.1007_s13171-024-00373-7
    DOI: 10.1007/s13171-024-00373-7
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    References listed on IDEAS

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    1. Pengcheng Ren & Guanfu Liu & Xiaolong Pu, 2023. "Generalized fiducial methods for testing the homogeneity of a three-sample problem with a mixture structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(5), pages 1094-1114, April.
    2. Glenn Heller & Jing Qin, 2001. "Pairwise Rank-Based Likelihood for Estimation and Inference on the Mixture Proportion," Biometrics, The International Biometric Society, vol. 57(3), pages 813-817, September.
    3. Guanfu Liu & Pengfei Li & Yukun Liu & Xiaolong Pu, 2020. "Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1064-1089, December.
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