Open Access
Translator Disclaimer
March 1995 Applications of the van Trees inequality: a Bayesian Cramér-Rao bound
Richard D. Gill, Boris Y. Levit
Bernoulli 1(1-2): 59-79 (March 1995).


We use a Bayesian version of the Cramér-Rao lower bound due to van Trees to give an elementary proof that the limiting distribution of any regular estimator cannot have a variance less than the classical information bound, under minimal regularity conditions. We also show how minimax convergence rates can be derived in various non- and semi-parametric problems from the van Trees inequality. Finally we develop multivariate versions of the inequality and give applications.


Download Citation

Richard D. Gill. Boris Y. Levit. "Applications of the van Trees inequality: a Bayesian Cramér-Rao bound." Bernoulli 1 (1-2) 59 - 79, March 1995.


Published: March 1995
First available in Project Euclid: 2 August 2007

zbMATH: 0830.62035
MathSciNet: MR1354456

Keywords: lower bounds , nonparametric estimation , Parameter estimation , quadratic risk , semi-parametric models

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability


Vol.1 • No. 1-2 • March 1995
Back to Top