Summary
This expository paper is concerned with lower bounds for the expected sample size EO(N) of an arbitrary sequential test whose error probabilities at two parameter points θ1. and θ2, do not exceed given numbers α1. and α2 where EO(N) is evaluated at a third parameter point θ0. The bounds in (1. 3) and (1.4) are shown to be attainable or nearly attainable in certain cases where θ0 lies between θ1. and θ2.
This research was partially supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49 (638)-261. Reproduction in whole or in part is permitted for any purpose of the United States Government. Part of this work was done while the author was a visiting professor at Stanford University.
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Bibliography
T.W. Anderson, “A modification of sequential analysis to reduce the sample size,” Ann. Math. Stat.
T.G. Donnelly, “A family of sequential tests,” Ph. D. dissertation, University of North Carolina, 1957.
Wassily Hoeffding, “A lower bound for the average sample number of a sequential test,” Ann. Math. Stat., Vol. 24 (1953), pp. 127–130.
Wassily Hoeffding, “Lower bounds for the expected sample size and the average risk of a sequential procedure.” Submitted for publication in Ann. Math. Stat.
J. Kiefer and Lionel Weiss, “Some properties of generalized sequential probability ratio tests,” Ann. Math. Stat., Vol. 28 (1957), pp. 57–74.
J. Seitz and K. Winkelbauer, “Remark concerning a paper of Kolmogorov and Prohorov,” Czechoslovak Math. J., Vol. 3(78) (1953), pp. 89–91 (Russian with English summary,).
Abraham Wald, “Differentiation under the expectation sign in the fundamental identity of sequential analysis,” Ann. Math. Stat., Vol. 17 (1946), pp. 493–497.
Abraham Wald, Sequential Analysis, John Wiley & Sons, Inc., New York, 1947.
Abraham Wald, Statistical Decision Functions, John Wiley & Sons, Inc., N. Y. 1950.
A. Wald and J. Wolfowitz, “Optimum character of the sequential probability ratio test,” Ann. Math. Stat., Vol. 19 (1948), pp. 326–339.
J. Wolfowitz, “The efficiency of sequential estimates and Wald’s equation for sequential processes,” Ann. Math. Stat., Vol. 18 (1947), pp. 215–230.
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© 1994 Springer Science+Business Media New York
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Hoeffding, W. (1994). Lower Bounds for the Expected Sample Size of a Sequential Test. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_24
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DOI: https://doi.org/10.1007/978-1-4612-0865-5_24
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