## The Annals of Statistics

### Bahadur Optimality of Sequential Experiments for Exponential Families

Stavros Kourouklis

#### Abstract

A theorem of Bahadur on the asymptotic optimality of the likelihood ratio statistic has been extended to sequential analysis by Berk and Brown (1978) in the context of testing one-sided hypotheses about the mean of a normal distribution with known variance. In this work, Bahadur's theorem is extended to sequential analysis for general hypotheses about the parameters of an exponential family of distributions. Specifically, it is shown that, under certain conditions, modifications of the likelihood ratio statistic analogous to those exhibited by Berk and Brown (1978) in the above normal context are optimal for any family of stopping times approaching $\infty$. These results indicate that Bahadur efficiency has a limited impact in sequential analysis.

#### Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1522-1527.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346808

Digital Object Identifier
doi:10.1214/aos/1176346808

Mathematical Reviews number (MathSciNet)
MR760704

Zentralblatt MATH identifier
0561.62071

JSTOR