Gill, Richard D.; Levit, Boris Y. Applications of the van Trees inequality: A Bayesian Cramér-Rao bound. (English) Zbl 0830.62035 Bernoulli 1, No. 1-2, 59-79 (1995). Summary: We use a Bayesian version of the Cramér-Rao lower bound due to H. L. van Trees [Detection, estimation, and modulation theory. Vol. I (1968; Zbl 0202.180)]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. Cited in 1 ReviewCited in 82 Documents MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference Keywords:quadratic risk; semi-parametric models; asymptotic global bounds; Cramer- Rao lower bound; limiting distribution; regular estimator; minimax convergence rates; van Trees inequality; multivariate versions Citations:Zbl 0202.180 PDFBibTeX XMLCite \textit{R. D. Gill} and \textit{B. Y. Levit}, Bernoulli 1, No. 1--2, 59--79 (1995; Zbl 0830.62035) Full Text: DOI Link