Springer Series in Statistics

Maximum Penalized Likelihood Estimation

Volume II: Regression

Authors: Eggermont, Paul P., LaRiccia, Vincent N.

  • 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
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eBook $149.00
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  • ISBN 978-0-387-68902-9
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  • ISBN 978-0-387-40267-3
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Softcover $189.00
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  • ISBN 978-1-4614-1712-5
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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 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.

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)


Table of contents (12 chapters)

  • Nonparametric Regression

    Eggermont, Paul P. B. (et al.)

    Pages 1-48

  • Smoothing Splines

    Eggermont, Paul P. B. (et al.)

    Pages 49-97

  • Kernel Estimators

    Eggermont, Paul P. B. (et al.)

    Pages 99-143

  • Sieves

    Eggermont, Paul P. B. (et al.)

    Pages 145-167

  • Local Polynomial Estimators

    Eggermont, Paul P. B. (et al.)

    Pages 169-203

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-68902-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-387-40267-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4614-1712-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Maximum Penalized Likelihood Estimation
Book Subtitle
Volume II: Regression
Authors
Series Title
Springer Series in Statistics
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-68902-9
DOI
10.1007/b12285
Hardcover ISBN
978-0-387-40267-3
Softcover ISBN
978-1-4614-1712-5
Series ISSN
0172-7397
Edition Number
1
Number of Pages
XX, 572
Topics