Nonparametric Smoothing and Lack-of-Fit Tests (Springer Series in Statistics) - Hardcover

Hart, Jeffrey

Hardcover

ISBN 10: 0387949801 ISBN 13: 9780387949802

Publisher: Springer, 1997

Synopsis

The The primary primary aim aim of of this this book book is is to to explore explore the the use use of of nonparametric nonparametric regres­ regres­ sion sion (i. e. , (i. e. , smoothing) smoothing) methodology methodology in in testing testing the the fit fit of of parametric parametric regression regression models. models. It It is is anticipated anticipated that that the the book book will will be be of of interest interest to to an an audience audience of of graduate graduate students, students, researchers researchers and and practitioners practitioners who who study study or or use use smooth­ smooth­ ing ing methodology. methodology. Chapters Chapters 2-4 2-4 serve serve as as a a general general introduction introduction to to smoothing smoothing in in the the case case of of a a single single design design variable. variable. The The emphasis emphasis in in these these chapters chapters is is on on estimation estimation of of regression regression curves, curves, with with hardly hardly any any mention mention of of the the lack-of­ lack-of­ fit fit problem. problem. As As such, such, Chapters Chapters 2-4 2-4 could could be be used used as as the the foundation foundation of of a a graduate graduate level level statistics statistics course course on on nonparametric nonparametric regression. regression.

About this title

Synopsis

A fundamental problem in statistical analysis is checking how well a particular probability model fits a set of observed data. In many settings, nonparametric smoothing methods provide a convenient and powerful means of testing model fit. Nonparametric Smoothing and Lack-of-Fit Tests explores the use of smoothing methods in testing the fit of parametric regression models. The book reviews many of the existing methods for testing lack-of-fit and also proposes a number of new methods. Both applied and theoretical aspects of the model checking problems are addressed. As such, the book should be of interest to practitioners of statistics and researchers investigating either lack-of-fit tests or nonparametric smoothing ideas. The first four chapters of the book are an introduction to the problem of estimating regression functions by nonparametric smoothers, primarily those of kernel and Fourier series type. This part of the book could be used as the foundation for a graduate level course on nonparametric function estimation. The prerequisites for a full appreciation of the book are a modest knowledge of calculus and some familiarity with the basics of mathematical statistics.

The less mathematically sophisticated reader will find Chapter 2 to be a comprehensible introduction to smoothing ideas and the rest of the book to be a valuable reference for both nonparametric function estimation and lack-of-fit tests. Jeffrey D. Hart is Professor of Statistics at Texas A&M University. He is an associate editor of the Journal of the American Statistical Association, an elected Fellow of the Institute of Mathematical Statistics, and winner of a distinguished teaching award at Texas A&M University.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0387949801
• ISBN 13: 9780387949802
• Binding: Hardcover
• Number of pages: 300