Skip to main content
SpringerLink
Log in

Estimation of density functionals

  • Estimation
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Given a sequence of independent random variables with densityf we estimate quantities θ of the form θ=∫ φ(f(x))dx, φ a known function, by inserting histograms and kernel density estimators for the unknownf. We obtain conditions for consistency and asymptotic normality and discuss the choice of cell size and bandwidth.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ahmad, I. A. (1976). On asymptotic properties of an estimate of a functional of a probability density,Scand. Actuar. J.,3, 176–181.

    Google Scholar 

  • Ahmad, I. A. and Lin, P. (1976). A nonparametric estimation of the entropy for absolutely continuous distributions,IEEE Trans. Inform. Theory,22, 372–375.

    Google Scholar 

  • Ahmad, I. A. and Lin, P. (1983). Consistency of a nonparametric estimator of a density functional,Metrika,30, 21–29.

    Google Scholar 

  • Bhattacharyya, G. K. and Roussas, G. G. (1969). Estimation of a certain functional of a probability density function,Skand. Aktuarietidskr.,3, 201–206.

    Google Scholar 

  • Bickel, P. J. and Ritov, Y. (1988). Estimating integrated squared density derivatives: sharp best order of convergence estimates,Sanya Ser. B,50, 381–393.

    Google Scholar 

  • Hall, P. and Marron, J. S. (1987). Estimation of integrated squared density derivatives,Statist. Probab. Lett.,6, 109–115.

    Google Scholar 

  • Jones, M. C. and Sheather, S. J. (1991). Using non-stochastic terms to advantage in kernel-based estimation of integrated squared derivatives,Statist. Probab. Lett.,11, 511–514.

    Google Scholar 

  • Pollard, D. (1984).Convergence of Stochastic Processes, Springer, New York.

    Google Scholar 

  • Prakasa Rao, B. L. S. (1983).Nonparametric Functional Estimation, Academic Press, New York.

    Google Scholar 

  • Schuster, E. F. (1974). On the rate of convergence of an estimate of a functional of a probability density,Scand. Actuarial J.,1, 103–107.

    Google Scholar 

  • Schweder, T. (1975). Window estimation of the asymptotic variance of rank estimators of location,Scand. J. Statist.,2, 113–126.

    Google Scholar 

  • Silverman, B. W. (1986).Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.

    Google Scholar 

  • van Es, B. (1992). Estimating functionals related to a density by a class of statistics based on spacings,Scand. J. Statist.,19, 61–72.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 17 (Mathematik-Informatik), Universität-GH Paderborn, 33095, Paderborn, Germany

    Rudolf Grübel

Authors
  1. Rudolf Grübel
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Grübel, R. Estimation of density functionals. Ann Inst Stat Math 46, 67–75 (1994). https://doi.org/10.1007/BF00773593

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773593

Key words and phrases

Search

Navigation