Abstract: 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) where and are the probability density functions of and , respectively. For the ordinary likelihood ratio statistic, we employ the assumption that for some , where and are the coefficients of the mixtures.
Key words and phrases: Mixture model, likelihood ratio test, modified likelihood ratio test, asymptotic distribution.