## The Annals of Statistics

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

Mohamed Tahir

#### 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

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