Information inequalities for the Bayes risk

DOI10.1214/aos/1176347867zbMath0722.62003OpenAlexW2044054651MaRDI QIDQ756309

Lawrence D. Brown, Lestaw Gajek

Publication date: 1990

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176347867

zbMATH Keywords

accuracyCramér-Rao inequalitylower boundsexponential familyexamplesBayes riskinformation inequalityscaled quadratic loss

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Point estimation (62F10) Bayesian inference (62F15) Bayesian problems; characterization of Bayes procedures (62C10) Statistical decision theory (62C99)

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A conversation with Larry Brown ⋮ Stimulus reference frame and neural coding precision ⋮ The heat equation and Stein's identity: connections, applications ⋮ Woodroofe's one-armed bandit problem revisited ⋮ Asymptotic comparison of some Bayesian information bounds ⋮ Attainments of the Bayesian information bounds ⋮ Superefficiency in nonparametric function estimation ⋮ Larry Brown's contributions to parametric inference, decision theory and foundations: a survey ⋮ Lower bounds on Bayes risks for estimating a normal variance: With applications ⋮ A van Trees inequality for estimators on manifolds ⋮ Cramér-Rao type integral inequalities for general loss functions ⋮ Ridge regression and asymptotic minimax estimation over spheres of growing dimension ⋮ Cramér--Rao bounds for posterior variances ⋮ Bhattacharyya-Type Information Inequality for the Bayes Risk ⋮ An Integral Bhattacharyya Type Bound for the Bayes Risk ⋮ Nonexponential Applications of a Global Cramèr-Rao Inequality ⋮ Lower bounds on the bayes risk eor statistical prediction problems ⋮ A lower bound for the bayes risk in the sequential case

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