Wavelet Methods in Statistics with R
Wavelet methods have recently undergone a rapid period of development with important implications for a number of disciplines including statistics. This book has three main objectives: (i) providing an introduction to wavelets and their uses in statistics
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Kurt Hornik Giovanni Parmigiani
Use R! Albert: Bayesian Computation with R Bivand/Pebesma/Gomez-Rubio: Applied Spatial Data Analysis with R ´ Claude:Morphometrics with R Cook/Swayne: Interactive and Dynamic Graphics for Data Analysis: With R and GGobi Hahne/Huber/Gentleman/Falcon: Bioconductor Case Studies Nason: Wavelet Methods in Statistics with R Paradis: Analysis of Phylogenetics and Evolution with R Peng/Dominici: Statistical Methods for Environmental Epidemiology with R: A Case Study in Air Pollution and Health Pfaff: Analysis of Integrated and Cointegrated Time Series with R, 2nd edition Sarkar: Lattice: Multivariate Data Visualization with R Spector: Data Manipulation with R
G.P. Nason
Wavelet Methods in Statistics with R
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G.P. Nason Department of Mathematics University of Bristol University Walk Bristol BS8 1TW United Kingdom [email protected] Series Editors: Robert Gentleman Program in Computational Biology Division of Public Health Sciences Fred Hutchinson Cancer Research Center 1100 Fairview Avenue, N. M2-B876 Seattle, Washington 98109 USA
Kurt Hornik Department of Statistik and Mathematik Wirtschaftsuniversität Wien Augasse 2-6 A-1090 Wien Austria
Giovanni Parmigiani The Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins University 550 North Broadway Baltimore, MD 21205-2011 USA
ISBN: 978-0-387-75960-9 DOI: 10.1007/978-0-387-75961-6
e-ISBN: 978-0-387-75961-6
Library of Congress Control Number: 2008931048 © 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com
To Philippa, Lucy, Suzannah, Mum and Dad.
Preface
When Zhou Enlai, Premier of the People’s Republic of China (1949–1976), was asked his opinion of the French Revolution (1789–1799) he replied “It’s too early to tell”, see Rosenberg (1999). I believe that the same can be said about wavelets. Although particular wavelets were discovered many years ago, the substantial body of literature that we might today call ‘wavelet theory’ began to be established during the 1980s. Wavelets were introduced into statistics during the late 1980s and early 1990s, and they were initially popular in the curve estimation literature. From there they spread in different ways to many areas such as survival analysis, statistical time series analysis, statistical image processing, inverse problems
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