MODIFIED ALGORITHM FOR FAST BANDWIDTH SELECTION OF KERNEL DENSITY ESTIMATION
A. V. Lapko1,2, V. A. Lapko1,2
1Institute of Computational Modelling SB RAS, Krasnoyarsk, Russia
2Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia
Keywords: kernel density estimation, fast optimization algorithm, bandwidth selection, antikurtosis coefficient, symmetric probability densities, second derivative of the probability density
Abstract
A modification of the fast algorithm of bandwidth selection of kernel functions in nonparametric probability density estimation of the Rosenblatt - Parzen type is proposed. Fast algorithms for optimizing the kernel density estimates can significantly reduce the time costs when selecting their bandwidth, as compared to the traditional approach. This is especially true when processing large volumes of statistical data. The basis of the proposed method is the analysis of the formula for the optimal calculation of the bandwidths of kernel functions and the detected dependence between the nonlinear functional of the second derivative of the reconstructed probability density and the antikurtosis coefficient. The proposed algorithm for bandwidth selection provides reduction in the probability density approximation error as compared to the traditional approach. The conclusions from the study are confirmed by the results of computational experiments. Particular attention is paid to the dependence of these properties on the amount of initial information.
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