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

Most of the researchers in the application areas usually use the EM algorithm to *nd estimators of the normal mixture distribution with unknown component speci*c variances without knowing much about the properties of the estimators. It is unclear for which situations the EM algorithm provides “good” estimators, 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 speci*c variance, while the number of components is *xed. 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 di9erences in the variances of the component distributions occur. c © 2002 Elsevier Science B.V. All rights reserved.