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Applications of the van Trees inequality: A Bayesian Cramér-Rao bound. (English) Zbl 0830.62035

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.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0202.180
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