A SIMPLE AND EFFECTIVE BANDWIDTH SELECTOR FOR KERNEL DENSITY-ESTIMATION

We present a simple and effective automated procedure for selecting th e bandwidth parameter h in kernel density estimation. The idea is to c hoose h such that parallel to F-n - F(n,h)parallel to(infinity) = cn(- 2/5) for an appropriate constant c, where F, is the empirical cdf, and F-n,F-h is the cdf for the kernel density estimator. The value of it is easy to compute and requires no prior information. Asymptotically t his gives the correct order of magnitude for h so as to minimize expec ted L(1)-resp. L(2)-error. We show by means of Atlantic City (Monte Ca rlo) simulations that this procedure works quite well for small sample sizes. We also discuss why one should expect the often observed negat ive correlation between the optimal bandwidth and the data driven band width selectors. Comparative results for some well-known data sets are also given.