A simple and effective bandwidth selector for kernel density estimation

We present a simple and effective automated procedure for selecting the bandwidth parameter h in kernel density estimation. The idea is to choose 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 this gives the correct order of magnitude for h so as to minimize expected L(1)-resp. L(2)-error. We show by means of Atlantic City (Monte Carlo) simulations that this procedure works quite well for small sample sizes. We also discuss why one should expect the often observed negative correlation between the optimal bandwidth and the data driven bandwidth selectors. Comparative results for some well-known data sets are also given.