FAST BANDWIDTH SELECTION FOR KERNEL PROBABILITY DENSITY ESTIMATION OF INDEPENDENT RANDOM VARIABLES
A. V. Lapko, V. A. Lapko
Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia
Keywords: kernel probability density estimation, fast algorithm for bandwidth selection, independent random variables, antikurtosis coefficient, single-modе symmetric distribution laws
Abstract
A method is proposed for fast bandwidth selection of kernel functions in nonparametric probability density estimation of a two-dimensional random variable with independent components. The distribution laws under study belong to the family of single-mode and symmetric probability densities. The possibility of their optimization is justified on the basis of the analysis of the asymptotic expressions of the mean square deviations of the components of a two-dimensional random variable. Each component is characterized by an optimal bandwidth of the kernel functions, which depends on the nonlinear functional of the probability density. Its functional dependence on the antikurtosis coefficient of a one-dimensional random variable is established. The effectiveness of the proposed technique is confirmed by the results of analytical studies.
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