Statistical Modeling by Wavelets

A comprehensive, step-by-step introduction to wavelets instatistics. What are wavelets? What makes them increasingly indispensable instatistical nonparametrics? Why are they suitable for "time-scale"applications? How are they used to solve such problems asdenoising, regression, or density estimation? Where can one findup-to-date information on these newly "discovered" mathematicalobjects? These are some of the questions Brani Vidakovic answers inStatistical Modeling by Wavelets. Providing a much-neededintroduction to the latest tools afforded statisticians by wavelettheory, Vidakovic compiles, organizes, and explains in depthresearch data previously available only in disparate journalarticles. He carefully balances both statistical and mathematicaltechniques, supplementing the material with a wealth of examples,more than 100 illustrations, and extensive references-with datasets and S-Plus wavelet overviews made available for downloadingover the Internet. Both introductory and data-oriented modelingtopics 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 instatistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus andalgebra, Statistical Modeling by Wavelets promises to become thestandard reference for statisticians and engineers seeking acomprehensive introduction to an emerging field.