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June, 1970 Stopping Times of SPRTS Based on Exchangeable Models
Robert H. Berk
Ann. Math. Statist. 41(3): 979-990 (June, 1970). DOI: 10.1214/aoms/1177696974


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.


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Robert H. Berk. "Stopping Times of SPRTS Based on Exchangeable Models." Ann. Math. Statist. 41 (3) 979 - 990, June, 1970.


Published: June, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0214.45202
MathSciNet: MR270503
Digital Object Identifier: 10.1214/aoms/1177696974

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 3 • June, 1970
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