Wavelet Methods in Statistics with R

Guy Nason

ISBN 10: 0387759603 / ISBN 13: 9780387759609

Published by Springer New York, Springer US Aug 2008, 2008

About this Item

Neuware -WhenZhouEnlai,PremierofthePeople¿sRepublicofChina(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 di erent ways to many areassuchassurvivalanalysis,statisticaltimeseriesanalysis,statisticalimage processing, inverse problems, and variance stabilization. The French Revolution was also the historical backdrop for the introd- tion of Fourier series which itself raised considerable objections from the s- enti c establishment of the day, see Westheimer (2001). Despite those early objections, we nd that, 200 years later, many new Fourier techniques are regularly being invented in many di erent elds. Wavelets are also a true s- enti c revolution. Some of their interesting features are easy to appreciate: e.g., multiscale, localization, or speed. Other important aspects, such as the unconditional basis property, deserve to be better known. I hope that this book, in some small way, enables the creation of many new wavelet methods.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 272 pp. Englisch.

Seller Inventory # 9780387759609

Bibliographic Details

• Title: Wavelet Methods in Statistics with R
• Publisher: Springer New York, Springer US Aug 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 0387759603
• ISBN 13: 9780387759609
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

This book contains information on how to tackle many important problems using a multiscale statistical approach. It focuses on how to use multiscale methods and discusses methodological and applied considerations.

From the Back Cover

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; (ii) acting as a quick and broad reference to many developments in the area; (iii) interspersing R code that enables the reader to learn the methods, to carry out their own analyses, and further develop their own ideas. The book code is designed to work with the freeware R package WaveThresh4, but the book can be read independently of R.

The book introduces the wavelet transform by starting with the simple Haar wavelet transform, and then builds to consider more general wavelets, complex-valued wavelets, non-decimated transforms, multidimensional wavelets, multiple wavelets, wavelet packets, boundary handling, and initialization. Later chapters consider a variety of wavelet-based nonparametric regression methods for different noise models and designs including density estimation, hazard rate estimation, and inverse problems; the use of wavelets for stationary and non-stationary time series analysis; and how wavelets might be used for variance estimation and intensity estimation for non-Gaussian sequences.

The book is aimed both at Masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers/users interested in statistical wavelet methods.

Guy Nason is Professor of Statistics at the University of Bristol. He has been actively involved in the development of various wavelet methods in statistics since 1993. He was awarded the Royal Statistical Society’s 2001 Guy Medal in Bronze for work on wavelets in statistics. He was the author of the first, free, generally available wavelet package for statistical purposes in S and R (WaveThresh2).