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September, 1984 Bounds for the Bayes Risk for Testing Sequentially the Sign of the Drift Parameter of a Wiener Process
Ashim Mallik, Yi-Ching Yao
Ann. Statist. 12(3): 1117-1123 (September, 1984). DOI: 10.1214/aos/1176346729

Abstract

Let $x(t)$ be a Wiener process with drift $\mu$ and variance 1 per unit time. The following problem is treated; test $H:\mu \leq 0$ vs. $A:\mu > 0$ with the loss function $|\mu|$ if the wrong decision is made and 0 otherwise, and with $c =$ cost of observation per unit time, where $\mu$ has a prior distribution which is normal with mean 0 and variance $\sigma^2_0$. An idea of Bickel and Yahav is followed to obtain a lower bound for the Bayes risk which is strict as $\sigma_0 \rightarrow \infty$ for all $c$. An upper bound is also derived.

Citation

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Ashim Mallik. Yi-Ching Yao. "Bounds for the Bayes Risk for Testing Sequentially the Sign of the Drift Parameter of a Wiener Process." Ann. Statist. 12 (3) 1117 - 1123, September, 1984. https://doi.org/10.1214/aos/1176346729

Information

Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0543.62057
MathSciNet: MR751300
Digital Object Identifier: 10.1214/aos/1176346729

Subjects:
Primary: 62L10
Secondary: 62C10

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • September, 1984
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