Estimation of heavy-tailed density functions with application to WWW-traffic

The estimation of heavy-tailed probability density function is an important tool for the description of the Web-traffic data and the solution of applied problems such as classification. The paper is devoted to the non-parametric estimation of a heavy-tailed probability density function by a variable bandwidth kernel estimator. Two approaches are used: (1) a preliminary transformation of the data to provide more accurate estimation of the density at the tail domain; (2) the discrepancy method based on the Kolmogorov-Smirnov statistic to evaluate the bandwidth of the kernel estimator. It is proved that the discrepancy method may provide the fastest achievable order of the mean squared error. An application to Web data analysis is presented