Bernoulli

  • Bernoulli
  • Volume 1, Number 1-2 (1995), 59-79.

Applications of the van Trees inequality: a Bayesian Cramér-Rao bound

Richard D. Gill and Boris Y. Levit

Full-text: Open access

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.

Article information

Source
Bernoulli Volume 1, Number 1-2 (1995), 59-79.

Dates
First available in Project Euclid: 2 August 2007

Permanent link to this document
http://projecteuclid.org/euclid.bj/1186078362

Mathematical Reviews number (MathSciNet)
MR1354456

Zentralblatt MATH identifier
0830.62035

Keywords
lower bounds nonparametric estimation parameter estimation quadratic risk semi-parametric models

Citation

Gill, Richard D.; Levit, Boris Y. Applications of the van Trees inequality: a Bayesian Cramér-Rao bound. Bernoulli 1 (1995), no. 1-2, 59--79. http://projecteuclid.org/euclid.bj/1186078362.


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