On the Use of Kernel Estimations in Data-Smoothing

Abstract

The use of kernel estimations in determination of the probability density and smoothing of the sequences is considered. Condition of the equality of the estimates of several central moments of the sample and moments determined for kernel estimation of the distribution density is used in the first case, the choice of the fuzziness index being thus simplified. Additionally, separate approximation of the branches of density estimations is used. The method of mode filtration is proposed to be used for smoothing the sequences. Determination of the smoothed value as an argument corresponding to the maximum of the density distribution estimation for the local section of the sequence provides tracing of the abrupt changes in the mean value of sequence and sift impulsive noise.