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The VPRT: A Sequential Testing Procedure Dominating the SPRT

Published online by Cambridge University Press:  11 February 2009

Noel Cressie  and
Peter B. Morgan
Noel Cressie
Affiliation:
Iowa State University
Peter B. Morgan
Affiliation:
SUNY at Buffalo
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Abstract

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

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Type
Articles
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Econometric Theory , Volume 9 , Issue 3 , June 1993 , pp. 431 - 450
Copyright
Copyright © Cambridge University Press 1993

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