Maximum Penalized Likelihood Estimation

1. Front Matter

   Pages i-xviii

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2. Nonparametric Regression

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 1-48

3. Smoothing Splines

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 49-97

4. Kernel Estimators

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 99-143

5. Sieves

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 145-167

6. Local Polynomial Estimators

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 169-203

7. Other Nonparametric Regression Problems

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 205-238

8. Smoothing Parameter Selection

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 239-283

9. Computing Nonparametric Estimators

   • Paul P. B. Eggermont, Vincent N. LaRiccia

   Pages 285-324

10. Kalman Filtering for Spline Smoothing

    • Paul P. B. Eggermont, Vincent N. LaRiccia

    Pages 325-372

11. Equivalent Kernels for Smoothing Splines

    • Paul P. B. Eggermont, Vincent N. LaRiccia

    Pages 373-424

12. Strong Approximation and Confidence Bands

    • Paul P. B. Eggermont, Vincent N. LaRiccia

    Pages 425-469

13. Nonparametric Regression in Action

    • Paul P. B. Eggermont, Vincent N. LaRiccia

    Pages 471-527

14. Back Matter

    Pages 1-40

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This is the second volume of a text on the theory and practice of maximum penalized likelihood estimation. It is intended for graduate students in s- tistics, operationsresearch, andappliedmathematics, aswellasresearchers and practitioners in the ?eld. The present volume was supposed to have a short chapter on nonparametric regression but was intended to deal mainly with inverse problems. However, the chapter on nonparametric regression kept growing to the point where it is now the only topic covered. Perhaps there will be a Volume III. It might even deal with inverse problems. But for now we are happy to have ?nished Volume II. The emphasis in this volume is on smoothing splines of arbitrary order, but other estimators (kernels, local and global polynomials) pass review as well. We study smoothing splines and local polynomials in the context of reproducing kernel Hilbert spaces. The connection between smoothing splines and reproducing kernels is of course well-known. The new twist is thatlettingtheinnerproductdependonthesmoothingparameteropensup new possibilities: It leads to asymptotically equivalent reproducing kernel estimators (without quali?cations) and thence, via uniform error bounds for kernel estimators, to uniform error bounds for smoothing splines and, via strong approximations, to con?dence bands for the unknown regression function. ItcameassomewhatofasurprisethatreproducingkernelHilbert space ideas also proved useful in the study of local polynomial estimators.

• Confidence bands
• Estimator
• Kalman filter for smoothing splines.
• Likelihood
• Local polynomials
• Nonparametric regression
• Reproducing kernel Hilbert spaces
• Smoothing splines
• Uniform error bounds
• data analysis
• expectation–maximization algorithm

From the reviews:

“This book is meant for specialized readers or graduate students interested in the theory, computation and application of Nonparametric Regression to real data, and the new contributions of the authors. … For mathematically mature readers, the book would be a delight to read. … The authors have not only written a scholarly and very readable book but provide major new methods and insights. … it would help evaluate the methods as well as lead to teachable notes for a graduate course.” (Jayanta K. Ghosh, International Statistical Review, Vol. 79 (1), 2011)

“This book is the second volume of a three-volume textbook in the Springer Series in Statistics. … The second volume also belongs to the literature on nonparametric statistical inference and concentrates mainly on nonparametric regression. … The book can be used for two main purposes: as a textbook for M.S./Ph.D. students in statistics, operations research, and applied mathematics, and as a tool for researchers and  practitioners in these fields who want to develop and to apply nonparametric regression methods.” (Yurij S. Kharin, Mathematical Reviews, Issue 2012 g)

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