Nonparametric Regression and Spline

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.

Randall L. Eubank is a Professor in the Department of Statistics at Texas AandM University, College Station

Preface

iii

Introduction

1

(26)

Regression Analysis

1

(9)

Nonparametric Regression

10

(11)

Linear Estimators

11

(3)

Consistency

14

(3)

Interval Estimation

17

(4)

Scope

21

(2)

Exercises

23

(4)

What Is a Good Estimator?

27

(44)

Performance Criteria

27

(10)

Estimating P(λ) and R(λ)

37

(13)

Order Selection In Hierarchical Models

50

(12)

Appendix

62

(1)

Exercises

63

(8)

Series Estimators

71

(84)

Introduction

71

(2)

Some Function Space Theory

73

(6)

Generalized Fourier Series Estimators

79

(6)

Trigonometric Series Estimators

85

(34)

Form of the Estimator

86

(4)

An Example

90

(7)

Consistency and Efficiency of the Estimator

97

(6)

Asymptotic Distribution Theory

103

(8)

Testing for No Effect

111

(8)

Polynomial Regression

119

(11)

Form of the Estimator

122

(3)

An Example

125

(2)

Large Sample Properties of the Estimator

127

(3)

Polynomial-Trigonometric Regression

130

(6)

Partially Linear Models

136

(7)

Appendix

143

(2)

Exercises

145

(10)

Kernel Estimators

155

(72)

Introduction

155

(1)

Kernel Estimators

156

(8)

Consistency

164

(11)

Selecting the Kernel Functions

175

(3)

Selecting the Bandwidth

178

(7)

Higher Order and Derivative Estimators

185

(4)

Locally Linear Estimators

189

(5)

Asymptotic Distribution Theory

194

(9)

Partially Linear Models

203

(7)

Random t's

210

(4)

Extensions

214

(2)

Exercises

216

(11)

Smoothing Splines

227

(64)

Introduction

227

(3)

Form of the Estimator

230

(9)

Selection of λ

239

(5)

Computation

244

(2)

Large Sample Properties

246

(14)

Smoothing Splines as Bayes Estimators

260

(13)

Extensions

273

(8)

Appendix

281

(3)

Exercises

284

(7)

Least-Squares Splines

291

(20)

Introduction

291

(1)

Form of the Estimator

291

(3)

Selecting λ

294

(5)

Computational Considerations

299

(2)

Asymptotic Analysis

301

(4)

Extensions

305

(3)

Exercises

308

(3)

Bibliography

311

(24)

Index

335

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Nonparametric Regression and Spline Smoothing, Second Edition

Summary

Author Biography

Table of Contents

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