Skip to main content
Log in

Estimation of a regression function by the parzen kernel-type density estimators

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

Summary

In this paper a theory of estimation of a regression function by the Parzen kernel-type density estimators is developed in the following points: 1) convergence of the estimators to the regression function at a continuous point, 2) convergence of the mean square error at a continuous point, and 3) the speed of the convergence in 2).

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Parzen, E. (1962). On estimation of a probability density function and mode,Ann. Math. Statist.,33, 1065–1076.

    MathSciNet  MATH  Google Scholar 

  2. Cacoullos, T. (1966). Estimation of a multivariate density,Ann. Inst. Statist. Math.,18, 179–189.

    Article  MathSciNet  MATH  Google Scholar 

  3. Schwartz, L. (1967).Cours d'analyse, I, Hermann, Paris.

    Google Scholar 

  4. Nadaraya, É. A. (1970). Remarks on non-parametric estimates for density functions and regression curves,Theory Prob. Appl.,15, 134–137.

    Article  MATH  Google Scholar 

  5. Ghosh, M. and Sen, P. K. (1970). On the almost sure convergence Von Mises' differentiable statistical functions,Calcutta Statist. Ass. Bull.,19, 41–44.

    MATH  Google Scholar 

  6. Ash, R. B. (1972).Real Analysis and Probability, Academic Press, New York.

    Google Scholar 

  7. Wahba, G. (1975), Optimal convergence properties of variable knot, kernel, and orthogonal series methods for density estimation,Ann. Statist.,3, 15–29.

    MathSciNet  MATH  Google Scholar 

Download references

Authors

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Noda, K. Estimation of a regression function by the parzen kernel-type density estimators. Ann Inst Stat Math 28, 221–234 (1976). https://doi.org/10.1007/BF02504741

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02504741

Keywords

Navigation