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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).

Abstract

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.

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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.

Information

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

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Vol.1 • No. 1-2 • March 1995
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