## The Annals of Mathematical Statistics

### Stopping Times of SPRTS Based on Exchangeable Models

Robert H. Berk

#### Abstract

Let $\mathbf{X}_1,\mathbf{X}_2,\cdots$ be a stochastic sequence and $\mathscr{P}$ and $\mathscr{L}$, two composite parametric hypotheses (models) under which the $\mathbf{X}_i$ are i.i.d. We consider SPRTs of $\mathscr{P}$ vs $\mathscr{L}$ that depend on a sequence of exchangeable densities. Included are SPRTs obtained by the method of weight-functions (Bayesian procedures) and many SPRTs obtained by invariance reduction. Conditions are established under which the stopping time of such a procedure is almost surely finite and has a nontrivial mgf. The ideas are illustrated using the sequential $t$-test.

#### Article information

Source
Ann. Math. Statist., Volume 41, Number 3 (1970), 979-990.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177696974

Digital Object Identifier
doi:10.1214/aoms/1177696974

Mathematical Reviews number (MathSciNet)
MR270503

Zentralblatt MATH identifier
0214.45202

JSTOR