EM-test for homogeneity in location-scale mixture model with a structural scale

Abstract

The testing problem for the homogeneity of a location-scale mixture model is fundamental for subsequent statistical inference. In this paper, we employ the EM-test method to test the homogeneity of two commonly encountered location-scale mixture models with a structural scale, and we also establish the theoretical properties of test statistics. Further, to enhance the reliability of the test, based on the computer experiments approach, we develop a Bartlett-corrected approximate distribution for the proposed test statistics. Through Monte Carlo studies and real data example, the effectiveness of the proposed testing procedure is compared with that of the classical one, especially for small or moderate sample sizes.

Keywords:

• Bartlett correction
• Computer experiments
• EM-test
• Homogeneity test
• Mixture model
• Small sample size

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by National Natural Science Foundation of China [No. 12101270], The Natural Science Foundation of the Jiangsu Higher Education Institutions of China [No. 22KJB110001], Ph.D. Teacher’s Research Support Project Foundation of Jiangsu Normal University [No. 21XFRX019], and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.