A SMOOTH NONPARAMETRIC ESTIMATE OF A MIXING DISTRIBUTION USING MIXTURES OF GAUSSIANS

We propose a method of estimating mixing distributions using maximum l ikelihood over the class of arbitrary mixtures of Gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h. This approach can lead to estimates of many s hapes, with smoothness controlled by parameter h. We show that the res ulting estimate will always be a finite mixture of Gaussians, each hav ing variance h. The nonparametric maximum likelihood estimate can be v iewed as a special case, with h = 0. The method can be extended to est imate multivariate mixing distributions. Examples and the results of a simulation study are presented.