Mallik, Ashim; Yao, Yi-Ching Bounds for the Bayes risk for testing sequentially the sign of the drift parameter of a Wiener process. (English) Zbl 0543.62057 Ann. Stat. 12, 1117-1123 (1984). Let x(t) be a Wiener process with drift \(\mu\) and variance 1 per unit time. Consider the following problem: 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 \(c=\cos t\) of observation per unit time, and \(\mu\) has a prior distribution which is normal with mean 0 and variance \(\sigma^ 2_ 0.\) The authors obtain a lower bound for the Bayes risk for the case of \(\sigma_ 0\) finite, and show that this lower bound is not asymptotically achievable as \(\sigma_ 0\to \infty\) for all \(c>0\). Furthermore, they show that the P. J. Bickel and J. A. Yahav’s lower bound [Tech. Rep. No.26, Dept. Statist., Stanford Univ. (1967)] is not asymptotically achievable as \(c\to 0\) for the case of \(\mu\) having the improper prior distribution. Reviewer: K.Uosaki MSC: 62L10 Sequential statistical analysis 62C10 Bayesian problems; characterization of Bayes procedures Keywords:stopping times; normal prior; Wiener process; lower bound for the Bayes risk × Cite Format Result Cite Review PDF Full Text: DOI