Statistics: Textbooks and Monographs. 157. New York, NY: Marcel Dekker, Inc. xi, 338 p. $ 165.00 (1999).
The book provides a unified account of the most popular approaches to nonparametric regression smoothing. It reflects the important changes in this field since the first edition was published in 1988, see the review Zbl 0702.62036. As the reordering of the book’s title shows, the main difference lies in a reduced emphasis on smoothing splines – only linear smoothing splines are studied in detail. This second edition contains revised and updated material on Fourier series type estimators and kernel estimators, on the connection between smoothing splines and both Fourier series and kernel estimators and on least-squares spline smoothing. Substantial changes occur in the chapter on series estimators; here a new approach leads to boundary corrected series estimators and provides estimators for partially linear models.
Further topics covered in the present text but not in the first edition include: regressograms, asymptotic and finite sample investigations of the properties of confidence intervals and bands, estimation in partially linear models, goodness-of-fit tests, results on local linear regression and new results on smoothing parameter selection procedures. As a reference, the book benefits statisticians who desire an overview of nonparametric regression methods, with worked-out special cases that exemplify general patterns or techniques.
Requiring only a working knowledge of calculus, mathematical statistics, matrix theory and some elementary large sample theory, the book is ideal for applied mathematicians, econometricians and engineers. As a text, it serves students as a useful learning guide with numerous examples and end-of-chapter problems, including data sets for analysis.