Learning from Data: Concepts, Theory, and Methods

This book consists of a collection of new wavelet techniques that can be used to explore several types of statistical problems, including but not limited to nonparametric regression, density estimation, and change-point problems. It provides an easy but solid introduction to available wavelet tools from an applied point of view. The main focus of this book seems to be development of the applied aspects of statistical functional estimation using a variety of wavelet methods. This book is intended as a reference for advanced undergraduateto graduate-level courses. It relies exclusively on several worked-out examples and provides step-by-step methods for most of the illustrated examples. This is de nitely a plus point for readers who want to get their hands dirty with wavelet tools. In fact, the reader may want to download the S-PLUS codes from the Web site cited by the author. The introductory chapters provide an overview of essential theory of wavelets, and these results are used throughout the text. Among the basic topics covered in this book are dyadic wavelets, time-frequency localization, wavelet transforms, frames, spline wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents generalizations and extensions to twodimensional wavelets and translation-invariant wavelet smoothing. The book requires a background in undergraduate calculus, linear algebra, and basic statistical theory. The “meat” part of the book lies in its Chapter 4, in which the author presents several “wavelet features and examples. ” The essential theory on wavelet decomposition and reconstruction is presented in a manner that is easy to follow and does not require substantial knowledge of advanced theory of functional analysis. The author then presents fundamental concepts of  lter representation and time-frequency localization. Finally, all of the aforementioned topics are then illustrated via several wavelet examples. Chapters 6 and 7 provide essential concepts for any researcher who is interested in statistical inference for wavelet-based models but is not necessarily an expert in either. The book has achieved its goal of presenting basic wavelet concepts in an understandable way to an audience familiar with the basic theory of statistics. The central theme of the book seems to focus on analyzing several statistical models using ready-made wavelet tools. The material covered in each chapter sometimes seems limited; emphasis on geometrical appeal to wavelets is not addressed. In summary, Essential Wavelets for Statistical Applications and Data Analysis does a good job of presenting wavelet tools to explain various aspects of statistical modeling. A very nice aspect of this book is that it provides a Web site reference that contains most additional resources, such as S-PLUS codes that were used to generate graphics used in the book. However, the book lacks the elegant geometrical approach of wavelet methods, but that is partially the nature of the material. Such fundamental geometrical concepts might turn out to be dif cult to follow for the beginners. Unfortunately, most books on wavelets are primarily accessible to research statisticians. This book presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of statistical and mathematical theory. The reader may also want to read a book by Vidakovic (1999) that also presents ideas similar to those developed in this one. I liked the book very much and would not hesitate to recommend its usage in a classroom as reference book for a course on statistical inference based on wavelet models.