On kNN Density Estimation

The k Nearest Neighb or (kNN) density estimator first for-malized by Loftsgaarden and Quesenb erry (1965) is central to a broad range of the literature on density estimation. It is knownto b e strongly uniformly consistent if k increases appropriatelywith the sample size. The contribution of this paper is to showthat the estimator is unbiased for finite sample size under assumptions regarding the lo cal variability of the density function. Moreover, significantly faster convergence to the true density in terms of mean squared error is obtained by replicating the estimate for small sample size. Finally, a mo dest number of nearest neighbors k is found to be efficient with respect to computation time.