Translator Disclaimer
2021 Test for homogeneity with unordered paired observations
Jiahua Chen, Pengfei Li, Jing Qin, Tao Yu
Author Affiliations +
Electron. J. Statist. 15(1): 1661-1694 (2021). DOI: 10.1214/21-EJS1817


In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is (X1,X2) but we observe only Y1=min{X1,X2} and Y2=max{X1,X2}, i.e., the subunit identities are not observed. We call (Y1,Y2) unordered paired observations. Based on unordered paired observations {(Y1i,Y2i)}i=1n, we are interested in whether the marginal distributions for X1 and X2 are identical. Testing methods are available in the literature under the assumptions that Var(X1)=Var(X2) and COV(X1,X2)=0. 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.

Funding Statement

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.


Download Citation

Jiahua Chen. Pengfei Li. Jing Qin. Tao Yu. "Test for homogeneity with unordered paired observations." Electron. J. Statist. 15 (1) 1661 - 1694, 2021.


Received: 1 January 2020; Published: 2021
First available in Project Euclid: 26 March 2021

Digital Object Identifier: 10.1214/21-EJS1817

Primary: 62F03, 62F05


Vol.15 • No. 1 • 2021
Back to Top