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Generalized fiducial methods for testing the homogeneity of a three-sample problem with a mixture structure

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  • Pengcheng Ren
  • Guanfu Liu
  • Xiaolong Pu

Abstract

Recently, the likelihood ratio (LR) test was proposed to test the homogeneity of a three-sample model with a mixture structure. Because of the presence of the mixture structure, the null limiting distribution of the LR test has a complicated supremum form, which leads to challenges in determining p-values. In addition, the LR test cannot control type-I errors well under small to moderate sample size. In this paper, we propose seven generalized fiducial methods to test the homogeneity of the three-sample model. Via simulation studies, we find that our methods perform significantly better than the LR test method in controlling the type-I errors under small to moderate sample size, while they have comparable powers in most cases. A halibut data example is used to illustrate the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:50:y:2023:i:5:p:1094-1114
    DOI: 10.1080/02664763.2021.2017414
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    Cited by:

    1. Yufan Wang & Xingzhong Xu, 2023. "A Posterior p -Value for Homogeneity Testing of the Three-Sample Problem," Mathematics, MDPI, vol. 11(18), pages 1-25, September.

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