Markovich Nonparametric Analysis of Univariate Heavy-Tailed Data

Research and Practice
1. Auflage 2008
ISBN: 978-0-470-72359-3
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 336 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Heavy-tailed distributions are typical for phenomena in complexmulti-component systems such as biometry, economics, ecologicalsystems, sociology, web access statistics, internet traffic,biblio-metrics, finance and business. The analysis of suchdistributions requires special methods of estimation due to theirspecific features. These are not only the slow decay to zero of thetail, but also the violation of Cramer's condition, possiblenon-existence of some moments, and sparse observations in the tailof the distribution.
The book focuses on the methods of statistical analysis ofheavy-tailed independent identically distributed random variablesby empirical samples of moderate sizes. It provides a detailedsurvey of classical results and recent developments in the theoryof nonparametric estimation of the probability density function,the tail index, the hazard rate and the renewal function.
Both asymptotical results, for example convergence rates of theestimates, and results for the samples of moderate sizes supportedby Monte-Carlo investigation, are considered. The text isillustrated by the application of the considered methodologies toreal data of web traffic measurements.

Autoren/Hrsg.

Markovich, Natalia

Über Autor(innen)

Natalia Markovich - Institute of Control Sciences,Russian Academy of Sciences, Moscow
Having been the Leading Scientist at the Institute of ControlSciences for the last eleven years, Dr Markovich has had muchexperience in this area. An extremely active member of thestatistical community, she has presented many seminars and invitedtalks, as well as being involved in numerous international researchprojects. She has published over 50 articles and has writtenchapters in two books, for Springer-Verlag and Elsevier.