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
Sharp asymptotics for isotonic regression
Download PDF
Download PDF
  • Published: February 2002

Sharp asymptotics for isotonic regression

  • Cécile Durot1 

Probability Theory and Related Fields volume 122, pages 222–240 (2002)Cite this article

Abstract.

 The asymptotic behavior of the isotonic estimator of a monotone regression function (that is the least-squares estimator under monotonicity restriction) is investigated. In particular it is proved that the ?1-distance between the isotonic estimator and the true function is of magnitude n -1/3. Moreover, it is proved that a centered version of this ?1-distance converges at the n 1/2 rate to a Gaussian variable with fixed variance.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Bâtiment 425, Université Paris Sud, 91405 Orsay Cedex, France. e-mail: cecile.durot@math.u-psud.fr, , , , , , FR

    Cécile Durot

Authors
  1. Cécile Durot
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 20 September 1999 / Revised version: 10 May 2001 / Published online: 19 December 2001

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Durot, C. Sharp asymptotics for isotonic regression. Probab Theory Relat Fields 122, 222–240 (2002). https://doi.org/10.1007/s004400100171

Download citation

  • Issue Date: February 2002

  • DOI: https://doi.org/10.1007/s004400100171

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

  • Asymptotic Behavior
  • Regression Function
  • True Function
  • Fixed Variance
  • Gaussian Variable
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