Estimation of heavy-tailed probability density function with applications to Web data
type: Item
instance of: scholarly article
title: Estimation of heavy-tailed probability density function with applications to Web data
zbMATH Open document ID: 1065.62059
DOI: 10.1007/BF02753913
author: R. E. Maiboroda
author: Natalia M. Markovich
published in: Computational Statistics
publication date: 2005-05-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 2169427
zbMATH Keywords: nonparametric density estimation
zbMATH Keywords: heavy-tailed density
zbMATH Keywords: kernel estimation
zbMATH Keywords: polygram
zbMATH Keywords: extreme value index
zbMATH Keywords: risk of misclassification
describes a project that uses: KernSmooth
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2169427