## The Annals of Statistics

### Nearly-Optimal Sequential Tests for Finitely Many Parameter Values

Gary Lorden

#### Abstract

Combinations of one-sided sequential probability ratio tests (SPRT's) are shown to be "nearly optimal" for problems involving a finite number of possible underlying distributions. Subject to error probability constraints, expected sample sizes (or weighted averages of them) are minimized to within $o(1)$ asymptotically. For sequential decision problems, simple explicit procedures are proposed which "do exactly what a Bayes solution would do" with probability approaching one as the cost per observation, $c$, goes to zero. Exact computations for a binomial testing problem show that efficiencies of about 97${\tt\%}$ are obtained in some "small-sample" cases.

#### Article information

Source
Ann. Statist., Volume 5, Number 1 (1977), 1-21.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343737

Digital Object Identifier
doi:10.1214/aos/1176343737

Mathematical Reviews number (MathSciNet)
MR438610

Zentralblatt MATH identifier
0386.62070

JSTOR