Nonparametric Least Squares Mixture Density Estimation

In this paper, we consider using nonparametric mixtures for density estimation. The mixture density estimation problem simply reduces to the problem of estimating a mixing distribution in the nonparametric mixture model. We focus on the least squares method for mixture density estimation problem. In a simulation experiment, the performance of the least squares mixture density estimator (MDE) and the kernel density estimator (KDE) is assessed by the mean integrated squared error. The performance improvement of MDE over KDE for some common densities is achieved by using cross-validation method for bandwidth selection.