Skip to main content
SpringerLink
Log in

A continuous form of post-stratification

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

Summary

The problem of estimating a given integral of a regression function is considered. The proposed estimate may be viewed as continuous analog of the post-stratified mean of sample survey theory. The asymptotic distribution of the estimate is derived, under regularity conditions, and an estimate of its variance suggested.

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

  1. Benedetti, J. K. (1977). On the nonparametric estimation of regression functions.J. R. Statist. Soc., B,39, 248–253.

    MathSciNet  MATH  Google Scholar 

  2. Chung, K. L. (1949). An estimate concerning the Kolmogorov limit distribution,Trans. Amer. Math. Soc.,67, 36–50.

    MathSciNet  MATH  Google Scholar 

  3. Clark, R. M. (1977). Non-parametric estimation of a smooth regression function,J. R. Statist. Soc., B,39, 107–113.

    MathSciNet  MATH  Google Scholar 

  4. Cochran, W. G. (1963).Sampling Techniques, J. Wiley, New York.

    MATH  Google Scholar 

  5. Feller, W. (1966).An Introduction to Probability Theory and its Applications, Vol. II, J. Wiley, New York.

    MATH  Google Scholar 

  6. Koksma, J. F. (1942). A general theorem from the theory of uniform distribution modulo 1,Mathematica Zutphen B,11, 7–11.

    MathSciNet  Google Scholar 

  7. Mosteller, F. and Tukey, J. W. (1977).Data Analysis and Regression, Addison-Wesley, Reading, Mass.

    Google Scholar 

  8. Nadaraya, E. A. (1964). On estimating regression,Theory Prob. Appl.,9, 141–142.

    Article  Google Scholar 

  9. Priestley, M. B. and Chao, M. T. (1972). Non-parametric function fitting.J. R. Statist. Soc., B,34, 385–392.

    MathSciNet  MATH  Google Scholar 

  10. Révész, P. (1976). On strong approximation of the multidimensional empirical process,Ann. Prob.,4, 729–743.

    Article  MathSciNet  Google Scholar 

  11. Rosenblatt, M. (1969). Conditional probability density and regression estimates, inMultivariate Analysis-II (ed. P. R. Krishnaiah), Academic, New York, 25–31.

    Google Scholar 

  12. Singh, R. S. (1977). Applications of estimators of a density and its derivatives to certain statistical problems.J. R. Statist. Soc., B,39, 357–363.

    MathSciNet  MATH  Google Scholar 

  13. Stone, C. (1975). Nearest neighbor estimators of a nonlinear regression function, inProc. Computer Sci. and Statistics: 8th Annual Symp. on the Interface, Los Angeles, Univ. of Calif., 413–418.

  14. Stone, C. (1977). Consistent nonparametric regression,Ann. Statist.,5, 595–620.

    Article  MathSciNet  Google Scholar 

  15. Watson, G. S. (1964). Smooth regression analysis,Sankhyã, A,26, 359–372.

    MathSciNet  MATH  Google Scholar 

  16. Zaremba, S. K. (1968). Some applications of multidimensional integration by parts,Ann. Polon. Math.,21, 85–96.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of California, Berkeley

    David R. Brillinger

Authors
  1. David R. Brillinger
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Brillinger, D.R. A continuous form of post-stratification. Ann Inst Stat Math 31, 271–277 (1979). https://doi.org/10.1007/BF02480282

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480282

Keywords

Search

Navigation