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Wavelets, Approximation, and Statistical Applications

  • Wolfgang Härdle
  • Gerard Kerkyacharian
  • Dominique Picard
  • Alexander Tsybakov

Part of the Lecture Notes in Statistics book series (LNS, volume 129)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 1-16
  3. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 17-23
  4. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 25-29
  5. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 31-34
  6. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 35-45
  7. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 47-58
  8. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 59-69
  9. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 71-100
  10. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 101-124
  11. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 125-191
  12. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 193-213
  13. Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
    Pages 215-235
  14. Back Matter
    Pages 237-268

About this book

Introduction

The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap­ proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process­ ing. Five years ago wavelet theory progressively appeared to be a power­ ful framework for nonparametric statistical problems. Efficient computa­ tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available software code. We hope therefore to address both theory and practice with this book and thus help to construct bridges between the different groups of scientists. This te. xt grew out of a French-German cooperation (Seminaire Paris­ Berlin, Seminar Berlin-Paris). This seminar brings together theoretical and applied statisticians from Berlin and Paris. This work originates in the first of these seminars organized in Garchy, Burgundy in 1994.

Keywords

DEX Invariant Lemma Oracle Sequence space Sobolev space adaptation availability code construction functions kernel signal processing turbulence wavelet

Authors and affiliations

  • Wolfgang Härdle
    • 1
  • Gerard Kerkyacharian
    • 2
  • Dominique Picard
    • 3
  • Alexander Tsybakov
    • 4
  1. 1.Wirtschaftswissenschaftliche Fakultät, Institut fär Statistik und ÖkonometrieHumboldt-Universität zu BerlinBerlinGermany
  2. 2.URA CNRS 1321 ModalUniversité Paris XNanterre CedexFrance
  3. 3.UFR Mathématique, URA CNRS 1321Université Paris VIIParis cedex 5France
  4. 4.Laboratoire de ProbabilitésUniversité Paris VIParis cedex 5France

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2222-4
  • Copyright Information Springer-Verlag New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98453-7
  • Online ISBN 978-1-4612-2222-4
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site