Skip to main content
Log in

The central limit theorem for maximum likelihood estimators of vector parameters: Locally uniform convergence

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Weak conditions are given which insure that the convergence in the central limit theorem for maximum likelihood estimators of vector parameters takes place uniformly on compact subsets of the parameter-space.

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. BHATTACHARYA, R.N. and RAO, R.R. Normal Approximation and Asymptotic Expansions. Wiley, New York, 1976.

    Google Scholar 

  2. BREIMAN, L. Probability. Addison-Wesley, Reading, Massachusetts, 1968.

    Google Scholar 

  3. KAUFMAN, S. Asymptotic efficiency of the maximum likelihood estimator. Ann. Inst. Stat. Math. 18, 155–178, 1966.

    Google Scholar 

  4. LE CAM, L. On the asymptotic theory of estimation and testing hypotheses. Proc. Third Berkeley Symp. Math. Statist. Prob. 1, 129–156, 1956.

    Google Scholar 

  5. MICHEL, R. and PFANZAGL, J. Asymptotic normality. Metrika 16, 188–205, 1970.

    Google Scholar 

  6. MICHEL, R. and PFANZAGL, J. The accuracy of the normal approximation for minimum contrast estimates. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 18, 73–84, 1971.

    Google Scholar 

  7. PARZEN, E. On uniform convergence of families of sequences of random variables. Univ. of California Publ. in Stat. 2, 23–54, 1954.

    Google Scholar 

  8. SAZONOV, V.V. On the multi-dimensional central limit theorem. Sankhyā 30A, 181–204, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Michel, R. The central limit theorem for maximum likelihood estimators of vector parameters: Locally uniform convergence. Manuscripta Math 23, 247–268 (1978). https://doi.org/10.1007/BF01171752

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01171752

Keywords

Navigation