Skip to main content
SpringerLink
Log in

Consistency of minimum contrast estimators in non-standard cases

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

In this paper we investigate the convergence of minimum contrast estimators to certain subsets of a “parameter space”. By means of these results it is possible to weaken a continuity condition which is usually needed to prove the consistency of maximum likelihood estimators.

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

  • Bahadur, R.R.: Some Limit Theorems in Statistics, Regional Conference Series in Applied Mathematics, Arowsmith 1971.

  • Berk, R.H.: Limiting behaviour of posterior distributions when the model is incorrect. Ann. Math. Statist.37, 1966, 51–58.

    Google Scholar 

  • Edgeworth, S.Y.: On the probable errors of frequency-constants. J. Roy. Stat. Soc.71, 1909, 381–397.

    Google Scholar 

  • Fisher, R.A.: The logic of inductive inference. J. Roy. Stat. Soc.98, 1935, 39–82.

    Google Scholar 

  • Godambe, V.P.: An optimum property of regular maximum likelihood estimators. Ann. Math. Statist.31, 1960, 1208–1212.

    Google Scholar 

  • Huber, P.J.: The behavior of maximum likelihood estimates under non-standard conditions. Proc. 5th Berkeley Symp. Math. Statist. Prob. Vol.1, 1967, 221–233.

    Google Scholar 

  • Kiefer, J., andJ. Wolfowitz: Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist.27, 1956, 884–906.

    Google Scholar 

  • Landers, D.: Existenz und Konsistenz von Maximum Likelihood Schätzern. University of Cologne, 1968.

  • LeCam, L.: On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. Univ. Calif. Publ. Statist.1, 1953, 277–330.

    Google Scholar 

  • Pfanzagl, J.: On the measurability and consistency of minimum contrast estimates. Metrika14, 1969, 249–272.

    Google Scholar 

  • Perlman, M.: On the strong consistency of approximate maximum likelihood estimators. Proc. 6th Berkeley Symp. Math. Statist. Prob. Vol. 1, 1970, 263–281.

    Google Scholar 

  • Reiss, R.-D.: On the measurability and consistency of maximum likelihood estimates for unimodal densities. Ann. Statist.1, 1973, 888–901.

    Google Scholar 

  • Wald, A.: Note on the consistency of the maximum likelihood estimates. Ann. Math. Statist.20, 1949, 595–601.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematische Stochastik der Universität Freiburg, Hermann-Herder-Straße 10, D-7800, Freiburg im Breisgau

    R. -D. Reiss

Authors
  1. R. -D. Reiss
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reiss, R.D. Consistency of minimum contrast estimators in non-standard cases. Metrika 25, 129–142 (1978). https://doi.org/10.1007/BF02204357

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02204357

Keywords

Search

Navigation