Wavelets and Statistics

1. Front Matter

   Pages ii-4

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2. Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure

   • Felix Abramovich, Yoav Benjamini

   Pages 5-14

3. Wavelets, spectrum analysis and 1/f processes

   • Patrice Abry, Paulo Gonçalvès, Patrick Flandrin

   Pages 15-29

4. Variance Function Estimation in Regression by Wavelet Methods

   • Anestis Antoniadis, Christian Lavergne

   Pages 31-42

5. Locally Self Similar Gaussian Processes

   • A. Benassi

   Pages 43-54

6. WaveLab and Reproducible Research

   • Jonathan B. Buckheit, David L. Donoho

   Pages 55-81

7. Extrema Reconstructions and Spline Smoothing: Variations on an Algorithm of Mallat & Zhong

   • René A. Carmona

   Pages 83-94

8. Identification of Chirps with Continuous Wavelet Transform

   • René Carmona, Wen Liang Hwang, Bruno Torrésani

   Pages 95-108

9. Nonlinear Approximation of Stochastic Processes

   • Albert Cohen, Jean-Pierre d’Ales

   Pages 109-123

10. Translation-Invariant De-Noising

    • R. R. Coifman, D. L. Donoho

    Pages 125-150

11. Estimating Wavelet Coefficients

    • Bernard Delyon, Anatoli Juditsky

    Pages 151-168

12. Nonparametric Supervised Image Segmentation by Energy Minimization using Wavelets

    • Jacques Istas

    Pages 169-192

13. On the Statistics of Best Bases Criteria

    • H. Krim, J.-C. Pesquet

    Pages 193-207

14. Discretized Wavelet Density Estimators for Continuous Time Stochastic Processes

    • Frédérique Leblanc

    Pages 209-224

15. Wavelets and Markov Random Fields in a Bayesian Framework

    • Maurits Malfait, Dirk Roose

    Pages 225-238

16. Micronde: a Matlab Wavelet Toolbox for Signals and Images

    • Yves Misiti, Michel Misiti, Georges Oppenheim, Jean-Michel Poggi

    Pages 239-259

17. Choice of the Threshold Parameter in Wavelet Function Estimation

    • G. P. Nason

    Pages 261-280

18. The Stationary Wavelet Transform and some Statistical Applications

    • G. P. Nason, B. W. Silverman

    Pages 281-299

19. Wavelet Thresholding: Beyond the Gaussian I.I.D. Situation

    • Michael H. Neumann, Rainer von Sachs

    Pages 301-329

20. L ²(0,1) Weak Convergence of the Empirical Process for Dependent Variables

    • Paulo Oliveira, Charles Suquet

    Pages 331-344

Despite its short history, wavelet theory has found applications in a remarkable diversity of disciplines: mathematics, physics, numerical analysis, signal processing, probability theory and statistics. The abundance of intriguing and useful features enjoyed by wavelet and wavelet packed transforms has led to their application to a wide range of statistical and signal processing problems. On November 16-18, 1994, a conference on Wavelets and Statistics was held at Villard de Lans, France, organized by the Institute IMAG-LMC, Grenoble, France. The meeting was the 15th in the series of the Rencontres Pranco-Belges des 8tatisticiens and was attended by 74 mathematicians from 12 different countries. Following tradition, both theoretical statistical results and practical contributions of this active field of statistical research were presented. The editors and the local organizers hope that this volume reflects the broad spectrum of the conference. as it includes 21 articles contributed by specialists in various areas in this field. The material compiled is fairly wide in scope and ranges from the development of new tools for non parametric curve estimation to applied problems, such as detection of transients in signal processing and image segmentation. The articles are arranged in alphabetical order by author rather than subject matter. However, to help the reader, a subjective classification of the articles is provided at the end of the book. Several articles of this volume are directly or indirectly concerned with several as­ pects of wavelet-based function estimation and signal denoising.

• Gaussian process
• Hypothese
• Markov random field
• Rang
• Variance
• Variation
• statistics
• stochastic processes

• Laboratoire IMAG-LMC, University Joseph Fourier, Grenoble Cedex, France

  Anestis Antoniadis

• Laboratoire MSS, University Paris-Sud, Orsay Cedex, France

  Georges Oppenheim

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