L-1-rate of convergence of smoothed histogram

We consider the smoothed histograms by gamma densities for an i.i.d. sample defined on the positive real line. Under sufficient conditions on the bandwidth and the density function, we obtain the asymptotic behavior, the lower and upper bound of the expected average absolute error of this estimator. The results of a simulation demonstrate the excellent performance of the gamma histogram. (c) 2007 Elsevier B.V. All rights reserved