Likelihood ratio test for homogeneity in normal mixtures in the presence of a structural parameter
Yong Song Qin, Bruce R. Smith · 2004
This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in normal mixture models in the presence of a structural parameter. The asymptotic null distributions of the ordinary likelihood ratio statistic and the modified likelihood ratio statistic are the same, having the probability density function(pdf) (1/2)g1(x)+(1/2)g2(x )w hereg1(x )a ndg2(x )a re the probability density functions of χ 2 and χ 2 , respectively. For the ordinary likelihood ratio statistic, we employ the assumption that min{α1 ,α 2 }≥ � for some 1/2 >�> 0, where α1 and α2 are the coefficients of the mixtures.