Nonparametric Estimation of Multivariate Mixtures

A multivariate mixture model is determined by three elements: the number of components, the mixing proportions, and the component distributions. Assuming that the number of components is given and that each mixture component has independent marginal distributions, we propose a nonparametric method to estimate the component distributions. The basic idea is to convert the estimation of component density functions to a problem of estimating the coordinates of the component density functions with respect to a good set of basis functions. Specifically, we construct a set of basis functions by using conditional density functions and try to recover the coordinates of component density functions with respect to this set of basis functions. Furthermore, we show that our estimator for the component density functions is consistent. Numerical studies are used to compare our algorithm with other existing nonparametric methods of estimating component distributions under the assumption of conditionally independent marginals.