Correction of Density Estimators that are not Densities

Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement-for-free procedure can, in particular, be applied for higher-order kernel estimators, classes of modern$h^{4}$bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the k-NN estimator, orthogonal expansion estimators, and for various recently developed semi-parametric density estimators.