Title: Taking advantage of the optimal kernel in nonparametric density estimation
Authors: Maria Isabel Borrajo - Universidade de Santiago de Compostela (Spain) [presenting]
Jose E Chacon - Universidad de Extremadura (Spain)
Alberto Rodriguez-Casal - University of Santiago de Compostela (Spain)
Abstract: Density estimation has been extensively studied, particularly in the context of nonparametric statistics. During the last decades many advances have been made: the introduction of the histogram, the kernel density estimator with all its variations and bandwidth selection methods, splines base methodology and so on. We propose a new density estimator based on a previous theory, which only requires the kernel to be a $L_2$-function. In this way, we let the kernel vary in shape and scale, and at the same time, we avoid the problem of bandwidth selection. The proposal is to use the empirical characteristic function by selecting a cut-off point to remove the extra noise that commonly appears in the tails; we define a new data-driven procedure to select this truncation point in the frequency domain and then apply Fourier transforms to obtain the target, i.e., the density estimation. The good performance of our proposal is illustrated in an extensive simulation study, in which we have also included the existing competitors.