Description
An exploration of 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, addressing both applied and theoretical aspects of the model checking problems. As such, the book is of interest to practitioners of statistics and researchers investigating either lack-of-fit tests or nonparametric smoothing ideas. The first four chapters introduce the problem of estimating regression functions by nonparametric smoothers, primarily those of kernel and Fourier series type, and 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. 1. Introduction.- 2. Some Basic Ideas of Smoothing.- 3. Statistical Properties of Smoothers.- 4. Data-Driven Choice of Smoothing Parameters.- 5. Classical Lack-of-Fit Tests.- 6. Lack-of-Fit Tests Based on Linear Smoothers.- 7. Testing for Association via Automated Order Selection.- 8. Data-Driven Lack-of-Fit Tests for General Parametric Models.- 9. Extending the Scope of Application.- 10. Some Examples.- A.2. Bounds for the Distribution of Tcusum.- References.
