Asymptotic properties of the EM algorithm estimate for normal mixture models with component specific variances

Abstract

Most of the researchers in the application areas usually use the EM algorithm to find estimators of the normal mixture distribution with unknown component specific variances without knowing much about the properties of the estimators. It is unclear for which situations the EM algorithm providesgoodestimators, good in the sense of statistical properties like consistency, bias, or mean square error. A simulation study is designed to investigate this problem. The scope of this study is set for the mixture model of normal distributions with component specific variance, while the number of components is fixed. The asymptotic properties of the EM algorithm estimate is investigated in each situation. The results show that the EM algorithm estimate does provide good asymptotic properties except for some situations in which the population means are quite close to each other and larger differences in the variances of the component distributions occur. © 2002 Elsevier Science B.V. All rights reserved.