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 the intensity of inhomogeneous Poisson processes via concentration inequalities
Download PDF
Download PDF
  • Published: May 2003

Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities

  • Patricia Reynaud-Bouret1 

Probability Theory and Related Fields volume 126, pages 103–153 (2003)Cite this article

  • 450 Accesses

  • 69 Citations

  • Metrics details

Abstract.

 In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities for suprema of integral functionals of Poisson processes which are analogous to Talagrand's inequalities for empirical processes.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Georgia Institute of Technology, School of Mathematics, Atlanta, GA 30332, USA. e-mail: Patricia.Reynaud@dma.ens.fr, , , , , , US

    Patricia Reynaud-Bouret

Authors
  1. Patricia Reynaud-Bouret
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 24 April 2001 / Revised version: 9 October 2002 / Published online: 15 April 2003

Mathematics Subject Classification (2000): 60E15, 62G05, 62G07

Key words or phrases: Inhomogeneous Poisson process – Concentration inequalities – Model selection – Penalized projection estimator – Adaptive estimation

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Reynaud-Bouret, P. Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities. Probab. Theory Relat. Fields 126, 103–153 (2003). https://doi.org/10.1007/s00440-003-0259-1

Download citation

  • Issue Date: May 2003

  • DOI: https://doi.org/10.1007/s00440-003-0259-1

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

  • Lower Bound
  • Poisson Process
  • Integral Functional
  • Empirical Process
  • Adaptive Estimation
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