Skip to main content
SpringerLink
Log in

Asymptotic efficiency of the Spearman estimator and characterizations of distributions

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

Summary

The Spearman estimator is designed to be a nonparametric estimator for the expectation of a tolerance distribution. We characterize the one-parameter families of distributions (the parameter being the mean of the distribution) for which the Spearman estimator has asymptotic efficiency one. In particular, when the parameter indexes the location, the characterizing distribution is the logistic distribution. In any other case of efficiency one, the family of distributions is given by certain transformations of a logistic distribution.

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. Berkson, J. (1953). A statistically precise and relatively simple method of estimating the bioassay with quantal response, based on the logistic function,J. Amer. Statist. Ass.,48, 565–599.

    MATH  Google Scholar 

  2. Brown, B. W. Jr. (1959). Some properties of the Spearman estimator in bioassay,Tech. Report No. 6, Department of Statistics, University of Minnesota, Minneapolis, Minnesota.

    Google Scholar 

  3. Brown, B. W. Jr. (1961). Some properties of the Spearman estimator in bioassay,Biometrika,48, 293–302.

    Article  Google Scholar 

  4. Chung, K. L. (1974).A Course in Probability Theory, Academic Press, New York.

    MATH  Google Scholar 

  5. Epstein, B. and Churchman, C. W. (1944). On the statistics of sensitivity data,Ann. Math. Statist.,15, 90–96.

    Article  MathSciNet  Google Scholar 

  6. Finney, D. J. (1950). The estimation of the mean of a normal tolerance distribution,Sankhyã,10, 341–360.

    MATH  Google Scholar 

  7. Finney, D. J. (1952). The estimation of the E.D. 50 for logistic response curve,Sankhyã,12, 121–136.

    MATH  Google Scholar 

  8. Finney,D. J. (1971).Probit Analysis, 3rd ed., Cambridge University Press.

  9. Gradshteyn, I. S. and Ryzhik, I. M. (1965).Table of Integrals and Products, Academic Press, New York.

    MATH  Google Scholar 

  10. Irwin, J. O. (1937). Statistical method applied to biological assays,J. R. Statist. Soc. (Suppl.),4, 1–60.

    MATH  Google Scholar 

  11. Miller, R. G. (1973). Nonparametric estimators of the mean tolerance in bioassay,Biometrika,60, 535–542.

    Article  MathSciNet  Google Scholar 

  12. Rustagi, J. S. (1976).Variational Methods in Statistics, Academic Press, New York.

    MATH  Google Scholar 

  13. Spearman, C. (1908). The method of ‘right and wrong cases’ (‘constant stimuli’) without Gauss' formula,Brit. J. Psychol.,2, 227–242.

    Google Scholar 

  14. Weaver, O. R. (1957). Using attributes for measurement of continuous variables in the rocket industry,Proc. 12th Midwest Quality Control Conference, American Society for Quality Control.

Download references

Author information

Author notes

  1. Bo. H. Lindqvist

    Present address: Norwegian Institute of Technology, Trondheim, Norway

Authors and Affiliations

  1. Stanford University, Stanford, USA

    Z. Govindarajulu & Bo. H. Lindqvist

Authors
  1. Z. Govindarajulu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo. H. Lindqvist
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author's research is supported by a Grant from the Office of Naval Research, Grant No. N00014-84-K-0184. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.

The author's research is supported by the Royal Norwegian Council for Scientific and Industrial Research.

About this article

Cite this article

Govindarajulu, Z., Lindqvist, B.H. Asymptotic efficiency of the Spearman estimator and characterizations of distributions. Ann Inst Stat Math 39, 349–361 (1987). https://doi.org/10.1007/BF02491473

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02491473

Key words and phrases

Search

Navigation