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 ex- tended 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 under- lying 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.

Discussion Paper / SFB 823;39/2014