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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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