Preface vii
Notations, Acronyms and Conventions xvii
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
19. Computing Nonparametric Estimators
1. Introduction 285
2. Cubic splines 285
3. Cubic smoothing splines 291
4. Relaxed boundary cubic splines 294
5. Higher-order smoothing splines 298
6. Other spline estimators 306
7. Active constraint set methods 313
8. Polynomials and local polynomials 319
9. Additional notes and comments 323
20. Kalman Filtering for Spline Smoothing
1. And now, something completely different 325
2. A simple example 333
3. Stochastic processes and reproducing kernels 338
4. Autoregressive models 350
5. State-space models 352
6. Kalman filtering for state-space models 355
7. Cholesky factorization via the Kalman filter 359
8. Diffuse initial states 363
9. Spline smoothing with the Kalman filter 366
10. Notes and comments 370
21. Equivalent Kernels for Smoothing Splines
1. Random designs 373
2. The reproducing kernels 380
3. Reproducing kernel density estimation 384
4. L2 error bounds 386
5. Equivalent kernels and uniform error bounds 388
6. The reproducing kernels are convolution-like 393
7. Convolution-like operators on Lp spaces 401
8. Boundary behavior and interior equivalence 409
9. The equivalent Nadaraya-Watson estimator 414
10. Additional notes and comments 421
22. Strong Approximation and Confidence Bands
1. Introduction 425
2. Normal approximation of iid noise 429
3. Confidence bands for smoothing splines 434
4. Normal approximation in the general case 437
5. Asymptotic distribution theory for uniform designs 446
6. Proofs of the various steps 452
7. Asymptotic 100% confidence bands 464
8. Additional notes and comments 468
23. Nonparametric Regression in Action
1. Introduction 471
2. Smoothing splines 475
3. Local polynomials 485
4. Smoothing splines versus local polynomials 495
5. Confidence bands 499
6. The Wood Thrush Data Set 510
7. The Wastewater Data Set 518
8. Additional notes and comments 527
Appendices
4. Bernstein’s inequality 529
5. The TVDUAL implementation 533
6. Solutions to Some Critical Exercises
1. Solutions to Chapter 13: Smoothing Splines 539
2. Solutions to Chapter 14: Kernel Estimators 540
3. Solutions to Chapter 17: Other Estimators 541
4. Solutions to Chapter 18: Smoothing Parameters 542
5. Solutions to Chapter 19: Computing 542
6. Solutions to Chapter 20: Kalman Filtering 543
7. Solutions to Chapter 21: Equivalent Kernels 546
References 549
Author Index 563
Subject Index 569

good book!!!!!!!!!!

Thanks a lot

a nice book!!!

能否找到第一卷：
Maximum Penalized Likelihood Estimation: Volume I: Density Estimation (Springer Series in Statistics)
期待第三卷！