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Title: Test for homogeneity with unordered paired observations
Authors: Chen, Jiahua
Li, Pengfei
Qin, Jing
Yu, Tao 
Keywords: Adjusted limiting distribution
Bartlett correction
Correlated unordered pairs
Likelihood ratio test
Two-sample test
Issue Date: 1-Jan-2021
Publisher: Institute of Mathematical Statistics
Citation: Chen, Jiahua, Li, Pengfei, Qin, Jing, Yu, Tao (2021-01-01). Test for homogeneity with unordered paired observations. Electronic Journal of Statistics 15 (1) : 1661-1694. ScholarBank@NUS Repository.
Rights: Attribution 4.0 International
Abstract: 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)}ni=1,weare 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)andcov(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. © 2021, Institute of Mathematical Statistics. All rights reserved.
Source Title: Electronic Journal of Statistics
ISSN: 1935-7524
DOI: 10.1214/21-ejs1817
Rights: Attribution 4.0 International
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