Practical Nonparametric Statistics

Chapter 7 covers, in depth, density estimators, thresholding, the use of nonlinear density estimators, multivariate wavelets estimators, and multiscale estimators. Chapter 8 provides an overview of Bayesian inference, which makes use of the data and prior information to select a less ad hoc shrinkage procedure for density estimation. Chapter 9 attempts to give an overview of the use of wavelet transform and its properties as applied to stochastic time series. In fact most of the chapter deals with the use of wavelets in estimating spectral densities, and then it briefly mentions the properties of the wavelets spectrum. Of pititular interest are the whitening properties of wavelet transform because they are approximate eigenfunctions to stationary stochastic time series. This is an important property for applied practitioners. I wish the author had expanded on this section and showed the similarity of wavelet transform to principal components analysis. Examples illustrating the use of this property for online modeling and monitoring are also lacking. Chapters 10-l 1 describe the use of wavelets to generate random densities and have references to miscellaneous other statistical applications of wavelets such as turbulence. This is not a book for casual readers of Technometrics as an introductory textbook on wavelets. As the author points out, “This book is aimed at graduate students in statistics or mathematics, and practicing statisticians” and “requires proficiency in advanced calculus.” For readers meeting these requirements, or those just familiar with wavelet theory, mathematically inclined, and wanting to learn more, the book will be enjoyable and interesting. 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.