Eubank R.L. Nonparametric Regression and Spline Smoothing

Marcel Dekker, 1999. — 356.When the first edition of this book, Spline Smoothing and Nonparametric Regression, appeared in 1988 it joined Prakasa Rao and Muller as the books concerning nonparametric regression which were widely available at that time. In the ensuing decade the number and variety of texts has increased substantially and many wonderful books are now available on data smoothing and related topics. These include texts on lo- local polynomial smoothing by Fan and Gjibels, treatises on kernel smoothing by Hardle and Wand and Jones, books on spline smoothing by Wahba and Green and Silverman and more general overviews by Scott and Simonoff.
The development of so many excellent smoothing related books in the last decade greatly influenced my perspective when preparing this second edition. There no longer appears to be a need for in-depth theoretical treatments of any particular smoothing methodology since these can be found in the books mentioned above, for example. Instead, I felt that an introductory treatment that opens the door for further study and investigation could be of some value and that is the viewpoint I have used in preparing the present book. It is intended primarily for a newcomer to the field of data smoothing whose knowledge of Statistics is at least that of, say, a second or third year Statistic's graduate student.
For maximum benefit, a reader of this book should have a good working knowledge of calculus, mathematical statistics, matrix theory and some elementary large sample theory (e.g., the law of large numbers, the Lindeberg-Feller central limit theorem and Slutsky's Theorem). The tools that are employed for proofs are not sophisticated and tend more toward grind-it- out linear thinking than mathematical elegance. This means that although the process of filling in omitted steps in an argument can be tedious, it can be accomplished given a determined attitude and a willingness to put pen to paper. My experience has been that students benefit more from completely understanding a simple, expandable special case of a problem than from vague cognition of some general framework. Thus, detailed analyses are typically provided only for canonical problems that allow for general developments through analogy and/or exercises.What Is a Good Estimator?
Series Estimators
Kernel Estimators
Smoothing Splines
Least-Squares Splines