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September, 1989 An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation
Mohamed Tahir
Ann. Statist. 17(3): 1335-1346 (September, 1989). DOI: 10.1214/aos/1176347273

Abstract

Let $\Omega$ be an interval and let $F_\omega, \omega \in \Omega,$ denote a one-parameter exponential family of probability distributions on $\mathscr{R} = (-\infty, \infty),$ each of which has a finite mean $\theta,$ depending on some unknown parameter $\omega \in \Omega.$ The main results of this paper determine an asymptotic lower bound for the local minimax regret, under a general smooth loss function and for a general class of estimators of $\theta.$ This bound is obtained by first determining the limit of the Bayes regret and then maximizing with respect to the prior distribution of $\omega.$

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Mohamed Tahir. "An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation." Ann. Statist. 17 (3) 1335 - 1346, September, 1989. https://doi.org/10.1214/aos/1176347273

Information

Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0681.62065
MathSciNet: MR1015155
Digital Object Identifier: 10.1214/aos/1176347273

Subjects:
Primary: 62L12

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • September, 1989
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