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
A law of the iterated logarithm for kernel estimators of regression functions
Download PDF
Download PDF
  • Published: September 1992

A law of the iterated logarithm for kernel estimators of regression functions

  • Zhao-Guo Chen1 &
  • Theo Gasser2 

Probability Theory and Related Fields volume 93, pages 285–296 (1992)Cite this article

  • 92 Accesses

  • 2 Citations

  • Metrics details

Summary

For fixed design regression data kernel estimation is widely used to estimate μ(v)(t), thev-th derivative of μ(t). Denoting such an estimator by\(\hat \mu _{nv} (t),\) this paper is concerned with the almost sure convergence of\(\hat \mu _{nv} (t) - E\hat \mu _{nv} (t)\). It is shown that under several inserting procedures a law of iterated logarithm holds.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • Cheng, K.F., Lin, P.E.: Nonparametric estimation of a regression function. Z. Wahrscheinlichkeitstheor. Verw. Geb.57, 223–233 (1981)

    Google Scholar 

  • Chen, Z.G.: An extension on Lai and Wei's law of the iterated logarithm with applications to time series and regression. J. Multivariate Anal32, 55–69 (1990)

    Google Scholar 

  • Gasser, T., Engel, J.: The choice of weights in nonparametric regression estimation. Biometrika77, 377–381 (1990)

    Google Scholar 

  • Gasser, T., Müller, H.G.: Kernel estimation of regression functions. In: Gasser, T., Rosenblatt, M. (eds.) Smoothing techniques for curve estimation, pp. 23–68. Berlin Heidelberg New York: Springer (1979)

    Google Scholar 

  • Gasser, T., Müller, H.G.: Estimating regression functions and derivatives by the kernel method. Scand. J. Stat.11, 171–185 (1984)

    Google Scholar 

  • Gasser, T., Müller, H.G.: Mammitzsch, V.: Kernels for nonparametric curve estimation. J. R. Stat. Soc. Ser. B47, 283–252 (1985)

    Google Scholar 

  • Härdle, W.: A law of the iterated logarithm for nonparametric regression function estimators. Ann. Stat.12, 624–635 (1984)

    Google Scholar 

  • Jennen-Steinmetz, C., Gasser, T.: A unifyign approach to nonparametric regression estimation. J. Am. Stat. Assoc.83, 1084–1089 (1988)

    Google Scholar 

  • Lai, T.L., Wei, C.Z.: A law of the iterated logarithm for double arrays of independent random variables with applications to regression and time series models. Ann. Probab.10, 320–335 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistical and Actuarial Sciences/WSC, The University of Western Ontario, London, Canada

    Zhao-Guo Chen

  2. Institut für Sozial-und Präventivmedizin, Universität Zürich, Sumatrastrasse 30, CH-8006, Zürich, Switzerland

    Theo Gasser

Authors
  1. Zhao-Guo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Theo Gasser
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chen, ZG., Gasser, T. A law of the iterated logarithm for kernel estimators of regression functions. Probab. Th. Rel. Fields 93, 285–296 (1992). https://doi.org/10.1007/BF01193053

Download citation

  • Received: 20 November 1990

  • Revised: 05 February 1992

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01193053

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

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Regression Function
  • Kernel 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