Title: Maximum Penalized Likelihood Estimation: Volume II: Regression
Authors: P.P.B. Eggermont and V.N. LaRiccia
Springer Series in Statistics, 2009
部分目录：

12. Nonparametric Regression
1. What and why? 1
2. Maximum penalized likelihood estimation 7
3. Measuring the accuracy and convergence rates 16
4. Smoothing splines and reproducing kernels 20
5. The local error in local polynomial estimation 26
6. Computation and the Bayesian view of splines 28
7. Smoothing parameter selection 35
8. Strong approximation and confidence bands 43
9. Additional notes and comments 48
13. Smoothing Splines
1. Introduction 49
2. Reproducing kernel Hilbert spaces 52
3. Existence and uniqueness of the smoothing spline 59
4. Mean integrated squared error 64
5. Boundary corrections 68
6. Relaxed boundary splines 72
7. Existence, uniqueness, and rates 83
8. Partially linear models 87
9. Estimating derivatives 95
10. Additional notes and comments 96
14. Kernel Estimators
1. Introduction 99
2. Mean integrated squared error 101
3. Boundary kernels 105
4. Asymptotic boundary behavior 110
5. Uniform error bounds for kernel estimators 114
6. Random designs and smoothing parameters 126
7. Uniform error bounds for smoothing splines 132
8. Additional notes and comments 143
15. Sieves
1. Introduction 145
2. Polynomials 148
3. Estimating derivatives 153
4. Trigonometric polynomials 155
5. Natural splines 161
6. Piecewise polynomials and locally adaptive designs 163
7. Additional notes and comments 167
16. Local Polynomial Estimators
1. Introduction 169
2. Pointwise versus local error 173
3. Decoupling the two sources of randomness 176
4. The local bias and variance after decoupling 181
5. Expected pointwise and global error bounds 183
6. The asymptotic behavior of the error 184
7. Refined asymptotic behavior of the bias 190
8. Uniform error bounds for local polynomials 195
9. Estimating derivatives 197
10. Nadaraya-Watson estimators 198
11. Additional notes and comments 202
17. Other Nonparametric Regression Problems
1. Introduction 205
2. Functions of bounded variation 208
3. Total-variation roughness penalization 216
4. Least-absolute-deviations splines: Generalities 221
5. Least-absolute-deviations splines: Error bounds 227
6. Reproducing kernel Hilbert space tricks 231
7. Heteroscedastic errors and binary regression 232
8. Additional notes and comments 236
18. Smoothing Parameter Selection
1. Notions of optimality 239
2. Mallows’ estimator and zero-trace estimators 244
3. Leave-one-out estimators and cross-validation 248
4. Coordinate-free cross-validation (GCV) 251
5. Derivatives and smooth estimation 256
6. Akaike’s optimality criterion 260
7. Heterogeneity 265
8. Local polynomials 270
9. Pointwise versus local error, again 275
10. Additional notes and comments 280