Summary
No matter which value t of a statistic T n has been observed the loss of information, in comparison with the original data, will asymptotically (as n→∞) always be the same: this statement is interpreted and proved in the framework of “comparison of experiments”, under assumptions commonly accepted in asymptotic statistics. The loss of information is described by the conditional experiments \(\{ \mathcal{L}_\theta (data|T_n = t): \theta \in \Theta \}\). These are shown to be all of the same “type”, as n→∞.
Article PDF
Similar content being viewed by others
References
Hájek, J.: A characterization of limiting distributions of regular estimates. Z. Wahrscheinlichkeitstheorie verw. Gebiete 14, 323–330 (1970)
Inagaki, N.: On the limiting distribution of a sequence of estimators with uniformity property. Ann. Inst. Statist. Math. 22, 1–13 (1970)
LeCam, L.: Locally asymptotically normal families of distributions. Univ. of California Publications in Statistics, Univ. of California Press, Berkeley and Los Angeles, Vol. 3, p. 37–98 (1960)
LeCam, L.: Sufficiency and approximate sufficiency. Ann. Math. Statist. 35, 1419–1455 (1964)
LeCam, L.: Limits of experiments. Proc. Sixth Berkeley Sympos. Math. Statist. Probab., Univ. of California Press, Berkeley and Los Angeles, Vol. 1, p. 245–261 (1972)
LeCam, L.: Notes on asymptotic methods in statistical decision theory. Centre de Recherches Mathématiques, Université de Montréal, Canada (Publication CRM-245) (1974)
LeCam, L.: unpublished book manuscript (1979)
Author information
Authors and Affiliations
Additional information
Research supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 123)
Rights and permissions
About this article
Cite this article
Ehm, W., Müller, D.W. Factorizing the information contained in an experiment, conditionally on the observed value of a statistic. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 121–134 (1983). https://doi.org/10.1007/BF00534999
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00534999