The Annals of Statistics

Bounds for the Bayes Risk for Testing Sequentially the Sign of the Drift Parameter of a Wiener Process

Ashim Mallik and Yi-Ching Yao

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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.

Article information

Source
Ann. Statist., Volume 12, Number 3 (1984), 1117-1123.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346729

Digital Object Identifier
doi:10.1214/aos/1176346729

Mathematical Reviews number (MathSciNet)
MR751300

Zentralblatt MATH identifier
0543.62057

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Sequential tests S.P.R.T. Bayes stopping times lower bound asymptotic expansion

Citation

Mallik, Ashim; Yao, Yi-Ching. Bounds for the Bayes Risk for Testing Sequentially the Sign of the Drift Parameter of a Wiener Process. Ann. Statist. 12 (1984), no. 3, 1117--1123. doi:10.1214/aos/1176346729. https://projecteuclid.org/euclid.aos/1176346729


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