Maximum Penalized Likelihood Estimation

Volume II: Regression

  • Vincent N. LaRiccia
  • Paul P.  Eggermont

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

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 1-48
  3. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 49-97
  4. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 99-143
  5. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 145-167
  6. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 169-203
  7. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 205-238
  8. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 239-283
  9. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 285-324
  10. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 325-372
  11. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 373-424
  12. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 425-469
  13. Paul P. B. Eggermont, Vincent N. LaRiccia
    Pages 471-527
  14. Back Matter
    Pages 1-40

About this book

Introduction

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 statistics, operations research and applied mathematics, as well as for researchers and practitioners in the field. The present volume deals with nonparametric regression.

The emphasis in this volume is on smoothing splines of arbitrary order, but other estimators (kernels, local and global polynomials) pass review as well. Smoothing splines and local polynomials are studied 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 that letting the innerproduct depend on the smoothing parameter opens up new possibilities. It leads to asymptotically equivalent reproducing kernel estimators (without qualifications), and thence, via uniform error bounds for kernel estimators, to uniform error bounds for smoothing splines and via strong approximations, to confidence bands for the unknown regression function.

The reason for studying smoothing splines of arbitrary order is that one wants to use them for data analysis. Regarding the actual computation, the usual scheme based on spline interpolation is useful for cubic smoothing splines only. For splines of arbitrary order, the Kalman filter is the most important method, the intricacies of which are explained in full. The authors also discuss simulation results for smoothing splines and local and global polynomials for a variety of test problems as well as results on confidence bands for the unknown regression function based on undersmoothed quintic smoothing splines with remarkably good coverage probabilities.

P.P.B. Eggermont and V.N. LaRiccia are with the Statistics Program of the Department of Food and Resource Economics in the College of Agriculture and Natural Resources at the University of Delaware, and the authors of Maximum Penalized Likelihood Estimation: Volume I: Density Estimation.

Keywords

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

Authors and affiliations

  • Vincent N. LaRiccia
  • Paul P.  Eggermont

There are no affiliations available

Bibliographic information

  • DOI https://doi.org/10.1007/b12285
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-40267-3
  • Online ISBN 978-0-387-68902-9
  • Series Print ISSN 0172-7397
  • About this book