Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T04:32:17.012Z Has data issue: false hasContentIssue false
  • English
  • Français

New Ways to Prove Central Limit Theorems

Published online by Cambridge University Press:  18 October 2010

David Pollard
David Pollard*
Affiliation:
Yale University
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes some techniques for proving asymptotic normality of statistics defined by maximization of random criterion function. The techniques are based on a combination of recent results from the theory of empirical processes and a method of Huber for the study of maximum likelihood estimators under nonstandard conditions.

Type
Research Article
Information
Econometric Theory , Volume 1 , Issue 3 , December 1985 , pp. 295 - 313
Copyright
Copyright © Cambridge University Press 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Billingsley, P. Convergence of Probability Measures. New York: Wiley,1968.Google Scholar
2. Daniels, H. E. The asymptotic efficiency of a maximum likelihood estimator. In Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 151–163. Berkeley: University of California, 1961.Google Scholar
3.Dudley, R. A course on empirical processes. Springer Lecture Notes in Mathematics 1097, pp. 1–142. New York: Springer, 1984.Google Scholar
4. Huber, P.J. Robust estimation of a location parameter. Annals of Mathematical Statistics 35 (1964): 73–101.10.1214/aoms/1177703732Google Scholar
5. Huber, P. J. The behavior of maximum likelihood estimates under nonstandard conditions In Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 221–233. Berkeley: University of California, 1967.Google Scholar
6. Ossiander, M. Weak convergence and a law of the iterated logarithm for processes indexed by points in a metric space. University of Washington, Technical Report No. 44, 1984.Google Scholar
7. Pollard, D. Convergence of Stochastic Processes. New York: Springer, 1984.10.1007/978-1-4612-5254-2Google Scholar
8. Vapnik, V. N. Cervonenkis, A. Ya., On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Its Applications 26 (1971): 532–553 10.1137/1126059Google Scholar