Essential Wavelets for Statistical Applications and Data Analysis

Presenting new developments in wavelet theory, this volume includes enough of the mathematics behind wavelets to enable applied statisticians and other users of statistics to understand and apply these methods to their own data. All the key elements of wavelets are brought out through examples, and various fundamental problems in statistics (nonparamtric regression, density estimation, etc) are discussed, with examples of how wavelets can be applied to this situation. I once heard the book by Meyer (1993) described as a'vulgarization'of wavelets. While this is true in one sense of the word, that of making a sub­ ject popular (Meyer's book is one of the early works written with the non­ specialist in mind), the implication seems to be that such an attempt some­ how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for­ mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way. I once heard the book by Meyer (1993) described as a "vulgarization" of wavelets. While this is true in one sense of the word, that of making a sub ject popular (Meyer's book is one of the early works written with the non specialist in mind), the implication seems to be that such an attempt some how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way. Prologue: Why Wavelets? -- 1. Wavelets: A Brief Introduction -- 2. Basic Smoothing Techniques -- 3. Elementary Statistical Applications -- 4. Wavelet Features And Examples -- 5. Wavelet-based Diagnostics -- 6. Some Practical Issues -- 7. Other Applications -- 8. Data Adaptive Wavelet Thresholding -- 9. Generalizations And Extensions. R. Todd Ogden. Includes Bibliographical References (p.[191]-198) And Index.