Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order

The problem of nonparametric estimation of a multivariate density function is addressed. In particular, a general class of estimators with favorable asymptotic performance (bias, variance, rate of convergence) is proposed. The proposed estimators are characterized by the flatness near the origin of the Fourier transform of the kernel and are actually shown to be exactlyN-consistent provided the density is sufficiently smooth.