Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T19:00:08.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Likelihood and Convergence

Published online by Cambridge University Press:  01 April 2022

Elliott Sober
Elliott Sober*
Affiliation:
Philosophy Department, University of Wisconsin, Madison
Get access Rights & Permissions [Opens in a new window]

Abstract

A common view among statisticians is that convergence (which statisticians call consistency) is a necessary property of an inference rule or estimator. In this paper, this view is challenged by appeal to an example in which a rule of inference has a likelihood rationale but is not convergent. The example helps clarify the significance of the likelihood concept in statistical inference.

Type
Research Article
Information
Philosophy of Science , Volume 55 , Issue 2 , June 1988 , pp. 228 - 237
Copyright
Copyright © 1988 by the Philosophy of Science Association

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.)

Footnotes

†

My thanks to Carter Denniston, A. W. F. Edwards, Ellery Eells, Joe Felsenstein, Isaac Levi, Steven Spielman, and the anonymous referees of this journal for useful discussion and to the National Science Foundation for financial assistance.

References

REFERENCES

Birnbaum, A. (1969), “Concepts of Statistical Evidence”, in Morgenbesser, S., Suppes, P., and White, M. (eds.), Philosophy, Science, and Method. New York: St. Martin's, pp. 112–143.Google Scholar
Edwards, A. (1972), Likelihood. Cambridge: Cambridge University Press.Google Scholar
Fisher, R. (1938), “Comment on H. Jeffrey's ‘Maximum Likelihood, Inverse Probability, and the Method of Moments‘”, Annals of Eugenics 8: 146–151.Google Scholar
Fisher, R. (1950), Statistical Methods for Research Workers, 11th edition. London: Oliver and Boyd.Google Scholar
Hacking, I. (1965), The Logic of Statistical Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kendall, M., and Stuart, A. (1973), The Advanced Theory of Statistics: Volume 2, 3rd edition. New York: Haffner Publishing Co.Google Scholar
Neyman, J. (1952), Lectures and Conferences on Mathematical Statistics and Probability, 2nd edition. Washington: Graduate School, U.S. Department of Agriculture.Google Scholar
Wald, A. (1949), “Note on the Consistency of the Maximum Likelihood Estimate”, Annals of Mathematical Statistics 20: 595–601.CrossRefGoogle Scholar