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

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.