The Annals of Statistics

On the Asymptotic Shape of Bayesian Sequential Tests of $\theta \leqq 0$ Versus $\theta > 0$ for Exponential Families

P. J. Bickel

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Abstract

We show that, in a weak sense, as the cost of observation tends to zero, the shape of the continuation region of the Bayes solution for the exponential family problem given above is approximated by that of a corresponding problem for the Wiener process with drift. The approach is an extension of that used in Bickel and Yahav, Proc. Sixth Berkeley Symp. Math. Statist. Prob. (1971).

Article information

Source
Ann. Statist., Volume 1, Number 2 (1973), 231-240.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342361

Digital Object Identifier
doi:10.1214/aos/1176342361

Mathematical Reviews number (MathSciNet)
MR378294

Zentralblatt MATH identifier
0255.62064

JSTOR
links.jstor.org

Citation

Bickel, P. J. On the Asymptotic Shape of Bayesian Sequential Tests of $\theta \leqq 0$ Versus $\theta > 0$ for Exponential Families. Ann. Statist. 1 (1973), no. 2, 231--240. doi:10.1214/aos/1176342361. https://projecteuclid.org/euclid.aos/1176342361


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