A comprehensive, step-by-step introduction to wavelets in statistics.

What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including:
* Continuous and discrete wavelet transformations.
* Statistical optimality properties of wavelet shrinkage.
* Theoretical aspects of wavelet density estimation.
* Bayesian modeling in the wavelet domain.
* Properties of wavelet-based random functions and densities.
* Several novel and important wavelet applications in statistics.
* Wavelet methods in time series.

Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.Mit Hilfe von Wavelets kann man lokale Phänomene exakter beschreiben - besonders trifft dies auf Probleme zu, für die Zeit und Bewegung eine Rolle spielen, wie beispielsweise die Akustik, die Auswertung seismischer Signale und die Bildverarbeitung. Diese ausgewogene Mischung statistischer und mathematischer Informationen will als Teil eines Einführungskurses verstanden sein, der Wavelets und deren statistische Behandlung zum Inhalt hat. Über 100 Strichzeichnungen, viele Übungen und Anwendungsbeispiele sowie ausführliche Literaturempfehlungen tragen zum Verständnis und zur Vertiefung des Stoffes bei. (04/99)