Multivariate parametric density estimation based on the modified Cramér-von Mises distance

In this paper, a novel distance-based density estimation method is proposed, which considers the overall density function in the goodness-of-fit. In detail, the parameters of Gaussian mixture densities are estimated from samples, based on the distance of the cumulative distributions over the entire state space. Due to the ambiguous definition of the standard multivariate cumulative distribution, the Localized Cumulative Distribution and a modified Cramér-von Mises distance measure are employed. A further contribution is the derivation of a simple-to-implement optimization procedure for the optimization problem. The proposed approach´s good performance in estimating arbitrary Gaussian mixture densities is shown in an experimental comparison to the Expectation Maximization algorithm for Gaussian mixture densities.