Contents

Preface iii
1 Introduction 1
1.1 Regression Analysis 1
1.2 Nonparametric Regression 10
1.2.1 Linear Estimators 11
1.2.2 Consistency 14
1.2.3 Interval Estimation 17
1.3 Scope 21
1.4 Exercises 23
2 What Is a Good Estimator? 27
2.1 Performance Criteria 27
2.2 Estimating P(A) and R(X) 37
2.3 Order Selection in Hierarchical Models 50
2.4 Appendix 62
2.5 Exercises 63
3 Series Estimators 71
3.1 Introduction 71
3.2 Some Function Space Theory 73
3.3 Generalized Fourier Series Estimators 79
3.4 Trigonometric Series Estimators 85
IX
CONTENTS
3.4.1 Form of the Estimator 86
3.4.2 An Example 90
3.4.3 Consistency and Efficiency of the Estimator 97
3.4.4 Asymptotic Distribution Theory 103
3.4.5 Testing for No Effect Ill
3.5 Polynomial Regression 119
3.5.1 Form of the Estimator 122
3.5.2 An Example 125
3.5.3 Large Sample Properties of the Estimator 127
3.6 Polynomial-Trigonometric Regression 130
3.7 Partially Linear Models 136
3.8 Appendix 143
3.9 Exercises 145
Kernel Estimators 155
4.1 Introduction 155
4.2 Kernel Estimators 156
4.3 Consistency 164
4.4 Selecting the Kernel Functions 175
4.5 Selecting the Bandwidth 178
4.6 Higher Order and Derivative Estimators 185
4.7 Locally Linear Estimators 189
4.8 Asymptotic Distribution Theory 194
4.9 Partially Linear Models 203
4.10 Random i's 210
4.11 Extensions 214
4.12 Exercises 216
Smoothing Splines 227
5.1 Introduction 227
5.2 Form of the Estimator 230
5.3 Selection of ? 239
5.4 Computation 244
5.5 Large Sample Properties 246
CONTENTS xi
5.6 Smoothing Splines as Bayes Estimators 260
5.7 Extensions 273
5.8 Appendix 281
5.9 Exercises 284
6 Least-Squares Splines 291
6.1 Introduction 291
6.2 Form of the Estimator 291
6.3 Selecting ? 294
6.4 Computational Considerations 299
6.5 Asymptotic Analysis 301
6.6 Extensions 305
6.7 Exercises 308
Bibliography 311
Index 335