Likelihood Ratio Test for Homogeneity in Normal Mixtures in the Presence of a Structural Parameter
نویسندگان
چکیده
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) where g1(x) and g2(x) are the probability density functions of χ2(1) and χ 2 (2), respectively. For the ordinary likelihood ratio statistic, we employ the assumption that min{α1, α2} ≥ for some 1/2 > > 0, where α1 and α2 are the coefficients of the mixtures.
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