Initializing normal mixtures of densities

It is well known that log-likelihood function for finite mixtures usually has local maxima and therefore the iterative EM algorithm for maximum-likelihood estimation of mixtures may be starting-point dependent. In this paper we propose a method of choosing initial parameters of mixtures which includes two stages: 1) computation of nonparametric optimally smoothed kernel estimate of the unknown density; and 2) optimal weighting of the smoothed kernel estimate using essential kernels as the initial estimate of the mixture. All the optimization tasks make use of a suitably modified EM algorithm. The properties and computational aspects of the proposed method are illustrated by a numerical example and some application possibilities are considered