Estimateurs efficaces et densités bayésiennes impropres. (Efficient estimators and improper Bayesian densities) (Q1117625)

In his study of the problem of Bayesian estimation, J. B. S. Haldane [cf. \textit{H. Jeffreys}, Theory of probability. 3rd ed. (1961; Zbl 0116.349)] has observed that maximum likelihood estimators can be represented as Bayes estimators (under quadratic loss function) with respect to improper prior densities. Here the authors show that this is not a special property of maximum likelihood estimators and that any unbiased efficient estimator can be considered as a Bayes estimator (under quadratic loss function) with Fisher information as the prior density. Under some general regularity conditions the Fisher information is known to be improper.