Skip to main content
SpringerLink
Log in
Book cover

Reproducing Kernel Hilbert Spaces in Probability and Statistics

  • Book
  • © 2004

Overview

Authors:
  1. Alain Berlinet

    1. Department of Mathematics, UMR CNRS 5030, University of Montpellier II, Montpellier cedex 05, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Christine Thomas-Agnan

    1. GREMAQ, UMR CNRS 5604, University of Toulouse I, Toulouse, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  2. Theory

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 1-54

  3. RKHS and Stochastic Processes

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 55-108

  4. Nonparametric Curve Estimation

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 109-183

  5. Measures and Random Measures

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 185-240

  6. Miscellaneous Applications

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 241-264

  7. Computational Aspects

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 265-291

  8. A Collection of Examples

    • Alain Berlinet, Christine Thomas-Agnan
    Pages 293-343

  9. Back Matter

    Pages 327-355
    Download chapter PDF
Back to top

Keywords

About this book

The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal solutions in one space are often usefully optimal in the other. The theory was born in complex function theory, abstracted and then accidently injected into Statistics; Manny Parzen as a graduate student at Berkeley was given a strip of paper containing his qualifying exam problem- It read "reproducing kernel Hilbert space"- In the 1950's this was a truly obscure topic. Parzen tracked it down and internalized the subject. Soon after, he applied it to problems with the following fla­ vor: consider estimating the mean functions of a gaussian process. The mean functions which cannot be distinguished with probability one are precisely the functions in the Hilbert space associated to the covariance kernel of the processes. Parzen's own lively account of his work on re­ producing kernels is charmingly told in his interview with H. Joseph Newton in Statistical Science, 17, 2002, p. 364-366. Parzen moved to Stanford and his infectious enthusiasm caught Jerry Sacks, Don Ylvisaker and Grace Wahba among others. Sacks and Ylvis­ aker applied the ideas to design problems such as the following. Sup­ pose (XdO

Authors and Affiliations

  • Department of Mathematics, UMR CNRS 5030, University of Montpellier II, Montpellier cedex 05, France

    Alain Berlinet

  • GREMAQ, UMR CNRS 5604, University of Toulouse I, Toulouse, France

    Christine Thomas-Agnan

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation