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.