Title: Bernstein Polynomial Model for Nonparametric Multivariate Density,
Abstract: In this paper, we study the Bernstein polynomial model for estimating the
multivariate distribution functions and densities with bounded support. As a
mixture model of multivariate beta distributions, the maximum (approximate)
likelihood estimate can be obtained using EM algorithm. A change-point method
of choosing optimal degrees of the proposed Bernstein polynomial model is
presented. Under some conditions the optimal rate of convergence in the mean
$\chi^2$-divergence of new density estimator is shown to be nearly parametric.
The method is illustrated by an application to a real data set. Finite sample
performance of the proposed method is also investigated by simulation study and
is shown to be much better than the kernel density estimate but close to the
parametric ones.