The Annals of Statistics

An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation

Mohamed Tahir

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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 $\omega.$

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1335-1346.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347273

Digital Object Identifier
doi:10.1214/aos/1176347273

Mathematical Reviews number (MathSciNet)
MR1015155

Zentralblatt MATH identifier
0681.62065

JSTOR
links.jstor.org

Subjects
Primary: 62L12: Sequential estimation

Keywords
Exponential families Bayes risk regret minimax theorem the martingale convergence theorem

Citation

Tahir, Mohamed. An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation. Ann. Statist. 17 (1989), no. 3, 1335--1346. doi:10.1214/aos/1176347273. https://projecteuclid.org/euclid.aos/1176347273


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