Automatic bandwidth selection for recursive kernel density estimators with length-biased data

Abstract

In this paper we propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm in the case of length-biased data. We compared our proposed plug-in method with the cross-validation method and the so-called smooth bootstrap bandwidth selector via simulations as well as a real data set. Results showed that, using the selected plug-in bandwidth and some special stepsizes, the proposed recursive estimators will be very competitive to the non-recursive one in terms of estimation error and much better in terms of computational costs.