Nonparametric Regression and Spline Smoothing

by Randall L. Eubank

Overview

Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.

Product Details

ISBN-13:	9780824793371
Publisher:	Taylor & Francis
Publication date:	02/09/1999
Series:	Statistics: A Series of Textbooks and Monographs , #157
Edition description:	Revised
Pages:	360
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Randall L. Eubank

Table of Contents

What is a good estimator?; series estimators; kernel estimators; smoothing splines; least-square splines.

Editorial Reviews

"Praise for the first edition. . . ...an excellent textbook for a graduate statistics course on nonparametric regression or as an introduction for someone wanting to learn about this area. "
—-Journal of the American Statistical Association
"...an important contribution to the dissemination of knowledge about nonparametric regression....Eubank's effort is highly tractable and contains many pragmatic tips without unduly sacrificing theoretical rigor. ...the second edition does include the many advances in nonparametric regression that have occurred since the eighties.... It is worthwhile to highlight the following merits of this book. Each chapter opens with a motivation for the topic understudy, and it identifies similarities with or differences from the classic parametric regression approach. Discussions of computation aspects are included wherever appropriate. Illustrative examples and exercises are abundant in each chapter.... ...the book was very well written, and...recommend[ed] to serve as reference and/or a textbook. "
—-Technometrics
"The book is a masterpiece: it is very clearly written, easy to follow and summarizes prominent research in approximation theory, based on mathematical statistics. ...strongly recommend[ed].... "
—-Bulletin GEodEsique

From the Publisher

Praise for the first edition... ...an excellent textbook for a graduate statistics course on nonparametric regression or as an introduction for someone wanting to learn about this area.

Journal of the American Statistical Association

...an important contribution to the dissemination of knowledge about nonparametric regression....Eubank's effort is highly tractable and contains many pragmatic tips without unduly sacrificing theoretical rigor. ...the second edition does include the many advances in nonparametric regression that have occurred since the eighties.... It is worthwhile to highlight the following merits of this book. Each chapter opens with a motivation for the topic understudy, and it identifies similarities with or differences from the classic parametric regression approach. Discussions of computation aspects are included wherever appropriate. Illustrative examples and exercises are abundant in each chapter.... ...the book was very well written, and...recommend[ed] to serve as reference and/or a textbook.

Technometrics

The book is a masterpiece: it is very clearly written, easy to follow and summarizes prominent research in approximation theory, based on mathematical statistics. ...strongly recommend[ed]....

Bulletin Geodesique

...Quite a lot has come about in the field of nonparametric smoothing in the last ten years and the second edition reflects this development....topics like regressograms, order selection for hierarchical models, properties of confidence intervals and bands, partially linear models, some new results on bandwidth selections and locally linear regression are now included or treated more extensively in the new edition.... ...this second edition of Eubank's book gives an excellent synopsis of the actual state of nonparametric regression and spline smoothing. The expositions are enriched with a lot of interesting examples showing practical applications and implications. Each chapter provides numerous exercises, covering theoretical as well as practical and computation aspects. The volume will be a winner on each statistical book shelf and indispensable for everybody working beyond linear regression.

Statistical Papers

...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-square spline smoothing. Substantial changes occur in the chapter of 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, good-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 patters or techniques. ...As a text, it serves students as a useful learning guide with numerous examples and end-of-chapter problems, including data sets for analysis.

Zentralblatt fur Mathematik

This textbook for a graduate level introductory course on data smoothing covers series estimators, kernel estimators, smoothing splines, and least-squares splines. The new edition deletes most of the asymptotic theory for smoothing splines and smoothing spline variants, and adds order selection for hierarchical models, estimation in partially linear models, polynomial-trigonometric regression, new results on bandwidth selection, and locally linear regression. The first edition was published as (1988). Annotation c. by Book News, Inc., Portland, Or.

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