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

Two new multiplicative bias correction techniques for nonparametric multivariate density estimation in the context of positively supported data are proposed. Both methods reach an optimal rate of convergence of the mean squared error of order O(n−8/(8+d))O(n−8/(8+d)), where dd is the dimension of the underlying data set. In addition, they overcome the boundary effect and their values are always non-negative. Asymptotic properties like bias and variance are investigated. Moreover, the performance of both estimators is studied in Monte Carlo simulations and in two real data examples.