The Annals of Mathematical Statistics

Stopping Times of SPRTS Based on Exchangeable Models

Robert H. Berk

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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

Permanent link to this document
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
links.jstor.org

Citation

Berk, Robert H. Stopping Times of SPRTS Based on Exchangeable Models. Ann. Math. Statist. 41 (1970), no. 3, 979--990. doi:10.1214/aoms/1177696974. https://projecteuclid.org/euclid.aoms/1177696974


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