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

Pengcheng Ren, Guanfu Liu and Xiaolong Pu

Journal of Applied Statistics, 2023, vol. 50, issue 5, 1094-1114

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.

Date: 2023
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DOI: 10.1080/02664763.2021.2017414

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