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Observations on a result in sequential analysis by P. Whittle

Published online by Cambridge University Press:  14 July 2016

J. C. Gittins
J. C. Gittins*
Affiliation:
University of Cambridge
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Abstract

In a series of papers Whittle has proposed locating the optimal boundary between the continuation region and the stopping region, in the no-overshoot approximation, for a class of sequential analysis problems by using the criterion that the gradient of the objective function must be continuous at the boundary. It is shown here that the result originally proposed by Whittle is not true in the generality which he supposed, and an indication is given of some of the circumstances in which it does hold.

Keywords

SEQUENTIAL DESIGNFREE BOUNDARY PROBLEMNO-OVERSHOOT APPROXIMATIONSTOPPING RULE
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 456 - 460
Copyright
Copyright © Applied Probability Trust 1973 

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References

Chernoff, H. (1961) Sequential tests for the mean of a normal distribution. Proc. 4th Berkeley Symp. on Statist. 79–91.Google Scholar
Chernoff, H. (1968) Optimal stochastic control. Sankhya A 30, 221–252.Google Scholar
Wetherill, G. B. (1966) Sequential Methods in Statistics. Methuen, London.Google Scholar
Whittle, P. (1964) Some general results in sequential analysis. Biometrika 51, 123–141.Google Scholar
Whittle, P. (1965) Some general results in sequential design. J. R. Statist. Soc. B 27, 371–396.Google Scholar
Whittle, P. (1969) Sequential decision processes with essential unobservables. Adv. Appl. Prob. 1, 271–287.Google Scholar
Whittle, P. (1973) An approximate characterization of optimal stopping boundaries. J. Appl. Prob. 10, 158–165.Google Scholar