Reweighted kernel density estimation

Standard kernel density estimation is subject to bias that can mask structure by flattening peaks and filling in troughs in the density. A number of methods of bias reduction have been proposed including approaches based on reweighting the contributions from the individual data points. We explore the potential of bias reduction by reweighting, and propose a new type of reweighted kernel density estimator in which the weights are defined by a cubic spline on the logit scale. The free parameters of this spline are optimized with respect to a leave-one-out performance criterion. Technical aspects of the implementation of our estimator are discussed and its finite sample performance is analysed through experiments with simulated and real data. The results are very encouraging, and suggest that our new methodology is capable of significantly greater bias reduction than existing reweighted density estimators.