Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods

In this article we propose two new Multiplicative Bias Correction (MBC) techniques for nonparametric multivariate density estimation. We deal with positively supported data but our results can easily be extended to the case of mixtures of bounded and unbounded supports. Both methods improve the optimal rate of convergence of the mean squared error up to O(n−8/(8+d)), where d is the dimension of the underlying data set. Moreover, they overcome the boundary effect near the origin and their values are always non-negative. We investigate asymptotic properties like bias and variance as well as the performance of our estimators in Monte Carlo Simulations and in a real data example.