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.
Similar content being viewed by others
References
BHATTACHARYA, R.N. and RAO, R.R. Normal Approximation and Asymptotic Expansions. Wiley, New York, 1976.
BREIMAN, L. Probability. Addison-Wesley, Reading, Massachusetts, 1968.
KAUFMAN, S. Asymptotic efficiency of the maximum likelihood estimator. Ann. Inst. Stat. Math. 18, 155–178, 1966.
LE CAM, L. On the asymptotic theory of estimation and testing hypotheses. Proc. Third Berkeley Symp. Math. Statist. Prob. 1, 129–156, 1956.
MICHEL, R. and PFANZAGL, J. Asymptotic normality. Metrika 16, 188–205, 1970.
MICHEL, R. and PFANZAGL, J. The accuracy of the normal approximation for minimum contrast estimates. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 18, 73–84, 1971.
PARZEN, E. On uniform convergence of families of sequences of random variables. Univ. of California Publ. in Stat. 2, 23–54, 1954.
SAZONOV, V.V. On the multi-dimensional central limit theorem. Sankhyā 30A, 181–204, 1968.
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01171752