Essential wavelets for statistical applications and data analysis.

*(English)*Zbl 0868.62033
Boston: Birkhäuser. xviii, 206 p. (1997).

The main goal of this book is to present the essential ideas required for a successful application of wavelet methods in data analysis and statistics. An introductory survey provides the bare necessities for understanding the basic principles of wavelet analysis, and more insight into some of the advantages inherent in wavelet analysis is given by describing basic algorithms, filtering properties, frequency localization concepts and examples of wavelet families.

A variety of statistical topics is discussed to demonstrate how and why wavelet methods work well in practice: Wavelet versions of the well-known smoothing techniques in nonparametric density and regression estimation are treated, diagnostic methods essential to a complete data analysis are described. Furthermore, the application of wavelets to the estimation of the spectral density in time series and to the general change-point-problem is covered, and an overview of current research in data dependent wavelet threshold selection is given.

The text is written in a non-theoretical style, the only mathematical prerequisite is a basic knowledge of undergraduate calculus, linear algebra and basic statistical theory. The clear and intuitive presentation makes the book ideal for a broad audience – including advanced undergraduate students, graduates and professionals, but also scientists and engineers who use data analysis methods.

A variety of statistical topics is discussed to demonstrate how and why wavelet methods work well in practice: Wavelet versions of the well-known smoothing techniques in nonparametric density and regression estimation are treated, diagnostic methods essential to a complete data analysis are described. Furthermore, the application of wavelets to the estimation of the spectral density in time series and to the general change-point-problem is covered, and an overview of current research in data dependent wavelet threshold selection is given.

The text is written in a non-theoretical style, the only mathematical prerequisite is a basic knowledge of undergraduate calculus, linear algebra and basic statistical theory. The clear and intuitive presentation makes the book ideal for a broad audience – including advanced undergraduate students, graduates and professionals, but also scientists and engineers who use data analysis methods.

Reviewer: H.Liero (Potsdam)

##### MSC:

62G07 | Density estimation |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |