Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations
Download PDF
Download PDF
  • Published: October 2000

Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations

  • Alexander Goldenshluger1 &
  • Sergei V. Pereverzev2 

Probability Theory and Related Fields volume 118, pages 169–186 (2000)Cite this article

  • 207 Accesses

  • 49 Citations

  • Metrics details

Abstract.

We consider adaptive estimating the value of a linear functional from indirect white noise observations. For a flexible approach, the problem is embedded in an abstract Hilbert scale. We develop an adaptive estimator that is rate optimal within a logarithmic factor simultaneously over a wide collection of balls in the Hilbert scale. It is shown that the proposed estimator has the best possible adaptive properties for a wide range of linear functionals. The case of discretized indirect white noise observations is studied, and the adaptive estimator in this setting is developed.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905, Israel. e-mail: goldensh@rstat.haifa.ac.il, , , , , , IL

    Alexander Goldenshluger

  2. Ukrainian Academy of Sciences, Institute of Mathematics, Tereshenkivska str. 3, 252601 Kiev-4, Ukraine. e-mail: serg-p@mail.kar.net, , , , , , UA

    Sergei V. Pereverzev

Authors
  1. Alexander Goldenshluger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei V. Pereverzev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 5 May 1999 / Revised version: 25 October 1999 / Published online: 5 September 2000

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Goldenshluger, A., Pereverzev, S. Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations. Probab Theory Relat Fields 118, 169–186 (2000). https://doi.org/10.1007/s440-000-8013-3

Download citation

  • Issue Date: October 2000

  • DOI: https://doi.org/10.1007/s440-000-8013-3

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • White Noise
  • Linear Functional
  • Flexible Approach
  • Noise Observation
  • Adaptive Estimate
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature