Wavelets and statistics. Proceedings of the 15th French-Belgian meeting of statisticians, held at Villard de Lans, France, November 16-18, 1994.

*(English)*Zbl 0824.00042
Lecture Notes in Statistics (Springer). 103. New York, NY: Springer- Verlag. 411 p. DM 74.00; öS 540.20; sFr 71.50 (1995).

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From the preface: Several articles of this volume are directly or indirectly concerned with several aspects of wavelet-based function estimation and signal denoising. Topics such as adaptative thresholding of wavelet coefficients, cross-validation and application of the stationary wavelet transform as an exploratory statistical method, together with their potential use in nonparametric regression, density estimation, and local spectral density estimation are discussed.

Nonlinear approximation methods based on wavelet and wavelet packet decompositions have been studied both in the context of statistics, compression, image analysis and signal processing algorithms, such as best basis selection and adaptive time-frequency decomposition. Many contributions are related to this topic.

Wavelet-based curve estimation methods have often been criticized for not being developed to handle nonuniform designs for predictors, heteroscedasticity for responses and non-i.i.d. situations. These problems are covered in several papers of this volume, as is the use of wavelet transforms for studying the spectrum analysis of \(1/f\) processes and establishing limit theorems for stochastic processes.

In addition to these articles on wavelet analysis and its applications in statistics and probability, three articles on software implementations for wavelet analysis, wavelet-packet analysis, cosine-packet analysis, and matching pursuit are included in these notes. The 24 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.

Indexed articles:

Abramovich, Felix; Benjamini, Yoav, Thresholding of wavelet coefficients as multiple hypotheses testing procedure, 5-14 [Zbl 0875.62081]

Abry, Patrice; Gonçalvès, Paulo; Flandrin, Patrick, Wavelets, spectrum analysis and \(1/f\) processes, 15-29 [Zbl 0828.62083]

Antoniadis, Anestis; Lavergne, Christian, Variance function estimation in regression by wavelet methods, 31-42 [Zbl 0828.62032]

Benassi, A., Locally self similar Gaussian processes, 43-54 [Zbl 0871.60032]

Buckheit, Jonathan B.; Donoho, David L., WaveLab and reproducible research, 55-81 [Zbl 0828.62001]

Carmona, René A., Extrema reconstructions and spline smoothing: Variations on an algorithm of Mallat \(\&\) Zhong, 83-94 [Zbl 0840.94004]

Carmona, René; Hwang, Wen Liang; Torrésani, Bruno, Identification of chirps with continuous wavelet transform, 95-108 [Zbl 0835.94007]

Cohen, Albert; d’Ales, Jean-Pierre, Nonlinear approximation of stochastic processes, 109-123 [Zbl 0828.60023]

Coifman, R. R.; Donoho, D. L., Translation-invariant de-noising, 125-150 [Zbl 0866.94008]

Delyon, Bernard; Juditsky, Anatoli, Estimating wavelet coefficients, 151-168 [Zbl 0832.62028]

Istas, Jacques, Nonparametric supervised image segmentation by energy minimization using wavelets, 169-192 [Zbl 0828.62037]

Krim, H.; Pesquet, J.-C., On the statistics of best bases criteria, 193-207 [Zbl 0828.62005]

Leblanc, Frédérique, Discretized wavelet density estimators for continuous time stochastic processes, 209-224 [Zbl 0828.62076]

Malfait, Maurits; Roose, Dirk, Wavelets and Markov random fields in a Bayesian framework, 225-238 [Zbl 0828.62086]

Misiti, Michel; Misiti, Yves; Oppenheim, Georges; Poggi, Jean-Michel, MICRONDE: a Matlab wavelet toolbox for signals and images, 239-259 [Zbl 1126.94301]

Nason, G. P., Choice of the threshold parameter in wavelet function estimation, 261-280 [Zbl 0875.62160]

Nason, G. P.; Silverman, B. W., The stationary wavelet transform and some statistical applications, 281-299 [Zbl 0828.62038]

Neumann, Michael H.; von Sachs, Rainer, Wavelet thresholding: Beyond the Gaussian i.i.d. situation, 301-329 [Zbl 0831.62071]

Oliveira, Paulo; Suquet, Charles, \(L^ 2(0,1)\) weak convergence of the empirical process for dependent variables, 331-344 [Zbl 0831.60037]

Taswell, Carl, Top-down and bottom-up tree search algorithms for selecting bases in wavelet packet transforms, 345-359 [Zbl 0842.94003]

Taswell, Carl, WavBox 4: a software toolbox for wavelet transforms and adaptive wavelet packet decompositions, 362-375 [Zbl 1126.94302]

Tate, Rosemary; Watson, Des; Eglen, Stephen, Using wavelets for classifying human in vivo magnetic resonance spectra, 377-383 [Zbl 0925.92084]

Tribouley, Karine, Adaptive density estimation, 385-395 [Zbl 0832.62037]

Zhang, Qinghua, Wavelets and regression analysis, 397-407 [Zbl 0829.62051]