Nonparametric Smoothing and Lack-of-Fit Tests / Edition 1

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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.

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Product Details

  • ISBN-13: 9780387949802
  • Publisher: Springer New York
  • Publication date: 7/31/1997
  • Series: Springer Series in Statistics
  • Edition description: 1997
  • Edition number: 1
  • Pages: 289
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.81 (d)

Table of Contents

1 Introduction 1
2 Some Basic Ideas of Smoothing 4
3 Statistical Properties of Smoothers 50
4 Data-Driven Choice of Smoothing Parameters 84
5 Classical Lack-of-Fit Tests 117
6 Lack-of-Fit Tests Based on Linear Smoothers 144
7 Testing for Association via Automated Order Selection 164
8 Data-Driven Lack-of-Fit Tests for General Parametric Models 208
9 Extending the Scope of Application 226
10 Some Examples 253
Appendix 267
References 271
Index 281
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