In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is but we observe only and , i.e., the subunit identities are not observed. We call unordered paired observations. Based on unordered paired observations , we are interested in whether the marginal distributions for and are identical. Testing methods are available in the literature under the assumptions that and . However, by extensive simulation studies, we observe that when one or both assumptions are violated, these methods have inflated type I errors or much lower powers. In this paper, we study the likelihood ratio test statistics for various scenarios and explore their limiting distributions without these restrictive assumptions. Furthermore, we develop Bartlett correction formulae for these statistics to enhance their precision when the sample size is not large. Simulation studies and real-data examples are used to illustrate the efficacy of the proposed methods.
Jiahua Chen has been supported in part by the National Natural Science Foundation of China Grant 11871419 and the Natural Sciences and Engineering Research Council of Canada Grant RGPIN-2019-04204. Pengfei Li has been supported in part by the Natural Sciences and Engineering Research Council of Canada Grant RGPIN-2020-04964. Tao Yu has been supported in part by Singapore Ministry Education Academic Research Tier 1 Funds (R-155-000-134-112; R-155-123-112; R-155-000-202-114) and the Ministry of Education of Singapore Grant MOE2014-T2-1-072.
The authors thank the editor, the associate editor, and the referees for constructive comments and suggestions that led to significant improvements in the paper.
"Test for homogeneity with unordered paired observations." Electron. J. Statist. 15 (1) 1661 - 1694, 2021. https://doi.org/10.1214/21-EJS1817