Skip to main content
SpringerLink
Log in

Robust Pitman-type estimators of location

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

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

References

  1. Birnbaum, A. (1961). Some theory and techniques for robust estimation, (Abstract),Ann. Math. Statist.,32, 622.

    Google Scholar 

  2. Birnbaum, A. and Laska, E. (1967). Optimal robustness: a general method, with applications to linear estimators of location,J. Amer. Statist. Assoc.,62, 1230–1240.

    Article  MATH  MathSciNet  Google Scholar 

  3. Birnbaum, A. and Miké, V. (1970). Asymptotically robust estimators of location,J. Amer. Statist. Assoc.,65, 1265–1282.

    Article  Google Scholar 

  4. Crow, E. L. and Siddiqui, M. M. (1967). Robust estimation of location,J. Amer. Statist. Assoc.,62, 353–389.

    Article  MathSciNet  Google Scholar 

  5. Gastwirth, J. L. and Cohen, M. L. (1968). The small sample behavior of some robust linear estimators of location,J. Amer. Statist. Assoc.,65, 946–973.

    Article  Google Scholar 

  6. Girshick, M. and Savage, L. J. (1951). Bayes and minimax estimates for quadratic loss functions,Proc. Second Berkeley Symp. Statist. Prob., 53–73, University of California Press.

  7. Govindarajulu, Z. (1966). Best linear estimates under symmetric censoring of the parameters of a double exponential population,J. Amer. Statist. Assoc.,61, 248–258.

    Article  MathSciNet  Google Scholar 

  8. Gupta, S. S., Qureishi, A. S. and Shah, B. K. (1967). Best linear unbiased estimators of the parameters of a logistic distribution using order statistics,Technometrics,9, 43–56.

    Article  MathSciNet  Google Scholar 

  9. Harris, T. E. and Tukey, J. W. (1949). Development of large sample measures of location and scale which are relatively insensitive to contamination, Report 31, Statistical Research Group, Princeton University.

  10. Hartigan, J. A. (1965). The asymptotically unbiased prior distribution,Ann. Math. Statist,36, 1137–1152.

    MATH  MathSciNet  Google Scholar 

  11. Karlin, S. (1958). Admissibility for estimation with quadratic loss,Ann. Math. Statist.,29, 406–436.

    MATH  MathSciNet  Google Scholar 

  12. LeCam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates,University of California Publications in Statistics,1, 277–330.

    MathSciNet  Google Scholar 

  13. LeCam, L. (1958). Les propriétés asymptotiques des solutions de Bayes,Publ. Inst. Statist. Univ. Paris,2, 17–35.

    MathSciNet  Google Scholar 

  14. Lindley, D. V. (1961). The use of prior probability distributions in statistical inference and decisions,Proc. Third Berkeley Symp. Math. Statist. Prob.,1, 453–468.

    MATH  MathSciNet  Google Scholar 

  15. Lindley, D. V. (1965).Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge University Press.

  16. Miké, V. (1967). Contributions to robust estimation, Doctoral dissertation, New York University.

  17. Miké, V. (1971). Efficiency-robust systematic linear estimators of location,J. Amer. Statist. Assoc.,66, 594–601.

    Article  MATH  Google Scholar 

  18. Miller, R. G. (1964). A trustworthy jackknife,Ann. Math. Statist.,35, 1594–1605.

    MATH  MathSciNet  Google Scholar 

  19. Pitman, E. J. G. (1939). The estimation of location and scale parameters of a continuous population of any form,Biometrika,30, 391–421.

    Article  MATH  Google Scholar 

  20. Rao, C. R. (1965).Linear Statistical Inference and Its Applications, Wiley, New York.

    MATH  Google Scholar 

  21. Stein, C. (1959). The admissibility of Pitman's estimator of a single location parameter,Ann. Math. Statist.,30, 970–979.

    MATH  MathSciNet  Google Scholar 

  22. Takeuchi, K. (1969). A uniformly asymptotically efficient robust estimator of a location parameter, Technical Report, Courant Institute of Mathematical Sciences, New York University.

  23. Wilks, S. S. (1963).Mathematical Statistics (2nd printing), Wiley, New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cornell University Medical College and Courant Institute of Mathematical Sciences New York University, New York, USA

    Valerie Miké

Authors
  1. Valerie Miké
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by the Office of Naval Research under Contract No. Nonr-285(38) by U.S. Public Health Service Research Grant No. 1 RO 1 GM16202-01 SSS, and by NCI Grant CA-08748.

About this article

Cite this article

Miké, V. Robust Pitman-type estimators of location. Ann Inst Stat Math 25, 65–86 (1973). https://doi.org/10.1007/BF02479360

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479360

Keywords

Search

Navigation