Pseudo-likelihood approach for parameter estimation in univariate normal mixture models

This article proposes a new approach for parameter estimation in univariate normal mixture distributions. The proposed method combines distance-based parameter estimation with maximum likelihood estimation and is therefore referred to as a pseudo-likelihood approach. In this pseudo-likelihood approach, the weights of the mixture components can be considered as functions of mixture component means and standard deviations. The proposed method has two main advantages in comparison to the traditional likelihood approach: (1) the pseudo-likelihood is always bounded, thus the global maximum exists; (2) since the mixture weights are functions of component means and standard deviations, the number of estimated parameters is reduced which may play an important role in models with many mixture components. We present several simulation examples to demonstrate the behaviour of the proposed method in different situations in comparison to other parameter estimation methods. It is interesting to observe that in some models, where it is more difficult to separate the components and the number of components is large, the pseudo-likelihood method beats the maximum likelihood method even for large sample sizes.