Estimation of heavy-tailed probability density function with applications to Web data
The authors discuss an approach to estimating probability density functions (PDF) using the so-called ``transform-retransform scheme'' which includes transformation of the data before application of specific estimation methods based on appropriate parametric or nonparametric approximation of the cumulative distribution functions (CDF) and estimation of the PDF of the original data applying the reverse transformation of the PDF estimate of the transformed data. In this context the authors focus on the following questions: what family of distributions is a reasonable approximation of the true CDF; which nonparametric estimate better maintains the tail decay rate of the true PDF. An application of the proposed PDF estimators to a classification problem is described, and their performance in cases of different heavy-tailed distributions is investigated by a simulation study. In particular, the PDF estimators are compared by their capacity to solve a classification problem. Simulation results and an application to Web data analysis are presented and discussed.
scientific article; zbMATH DE number 2169427