Statistical Modeling by Wavelets

ISBN-13: 9780471293651 / Angielski / Twarda / 1999 / 408 str.

Brani Vidakovic

Opis

Wavelets provide the ability to describe local phenomena more accurately, especially where time and movement are vital, such as acoustics and seismic signals and in image analysis. Carefully balancing both statistical and mathematical techniques, this text is intended for use as part of an introductory course concerned with the interface of wavelets and statistical inference. It incorporates examples and applications, numerous computational exercises and problem/homework sets, and extensive references at the end of each chapter. Several novel and important wavelet applications in statistics are covered, including deconvolution, approximate factor analysis, spectral density estimation, wavelet classificatory, pursuit methods, and maximum-modulus methods. It displays data sets and S+ wavelets overviews in the appendix.

Recenzje

It is well written and organized with compact derivations and extensive references and can serve as a very good reference on the exciting topic of wavelets. (Technometrics, August 2000, Vol. 42, No. 3) It is clearly an important and valuable addition to the area and deserves to be widely known and used.––(Statistics and Decisions, Volume 19, No.1, 2001)

"...an important and valuable addition to the area and deserves to be widely known and used." (Statistics and Decisions, Vol. 19, No. 1)

"It is clearly an important and valuable addition to the area and deserves to be widely known and used..." (Statistics & Decisions, Vol 19/1, 2001)

Spis treści

Prerequisites.

Wavelets.

Discrete Wavelet Transformations.

Some Generalizations.

Wavelet Shrinkage.

Density Estimation.

Bayesian Methods in Wavelets.

Wavelets and Random Processes.

Wavelet–Based Random Variables and Densities.

Miscellaneous Statistical Applications.

References.

Indexes.

O autorze

BRANI VIDAKOVIC, PhD, is Assistant Professor at the Institute of Statistics and Decision Sciences at Duke University.

Blurb

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.