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The VPRT: A Sequential Testing Procedure Dominating the SPRT


  • Cressie, Noel
  • Morgan, Peter B.


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.

Suggested Citation

  • Cressie, Noel & Morgan, Peter B., 1993. "The VPRT: A Sequential Testing Procedure Dominating the SPRT," Econometric Theory, Cambridge University Press, vol. 9(3), pages 431-450, June.
  • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:431-450_00

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    Cited by:

    1. H. Heyer & K. Elworthy & N. Cressie & R. Williams & H. Büning & R. Schassberger & H. Lütkepohl, 1995. "Book reviews," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 139-148, December.
    2. Forsyth, Margaret, 1997. "The Economics of Site Investigation for Groundwater Protection: Sequential Decision Making under Uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 34(1), pages 1-31, September.
    3. Giuseppe Moscarini & Lones Smith, 1998. "Wald Revisited: The Optimal Level of Experimentation," Cowles Foundation Discussion Papers 1176, Cowles Foundation for Research in Economics, Yale University.
    4. Yannis Bilias, 2000. "Sequential testing of duration data: the case of the Pennsylvania 'reemployment bonus' experiment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 575-594.

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