ON THE L-1-ERROR IN HISTOGRAM DENSITY-ESTIMATION - THE MULTIDIMENSIONAL CASE

Under some smoothness and tail conditions on the density the rate of c onvergence of the expected L-1-error of the classical histogram densit y estimator is calculated in any dimension. The asymptotic distributio n of the standardized L-1-error is derived under minimal conditions. I n particular, a sharp uniform rate for the variance of the error is es tablished and explicit representations of the asymptotic variance of t he error are given.