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Maximum Penalized Likelihood Estimation

Volume II: Regression

  • Book
  • © 2009

Overview

Authors:
  1. Vincent N. LaRiccia
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    You can also search for this author in PubMed   Google Scholar

  2. Paul P. Eggermont
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  • Fully develops the theory of convex minimization problems to obtain convergence rates
  • Includes simulation studies and analyses of classical data sets using fully automatic (data driven) procedures
  • Many topics appear for the first time in textbook form
  • Intended for graduate students as well as researchers and practitioners in the field of statistics and industrial mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  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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Keywords

About this book

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.

Reviews

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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