EM-test for homogeneity in a two-sample problem with a mixture structure

Guanfu Liu; Yuejiao Fu; Jianjun Zhang; Xiaolong Pu; Boying Wang

doi:10.1080/02664763.2019.1652254

EM-test for homogeneity in a two-sample problem with a mixture structure

J Appl Stat. 2019 Aug 8;47(4):724-738. doi: 10.1080/02664763.2019.1652254. eCollection 2020.

Authors

Guanfu Liu¹, Yuejiao Fu², Jianjun Zhang³, Xiaolong Pu⁴, Boying Wang⁴

Affiliations

¹ School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, People's Republic of China.
² Department of Mathematics and Statistics, York University, Toronto, Canada.
³ Department of Mathematics, University of North Texas, Denton, TX, USA.
⁴ School of Statistics, East China Normal University, Shanghai, People's Republic of China.

Abstract

In many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

Keywords: EM-test; homogeneity test; limiting distribution; scale mixtures; two-sample problem.

Grants and funding

Dr. Liu's and Professor Pu's research was supported by grants from the National Natural Science Foundation of China (11801359, 11801210, 11701360, 11771145). Professor Fu's research was supported by Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.