Fixed width interval estimation for the reciprocal drift of Brownian motion

Abstract

Let b(t), 0t[mu]. The problem of setting a fixed width confidence interval for [theta]=1[+45 degree rule][mu] is considered. The intervals studied are of the form , where [zeta] is a stopping time and . Stopping times [tau]h are derived s o that these intervals have coverage probabilities converging to a set value [gamma] as h-->0. This convergence is uniform for [mu] near 0. Asymptotic optimality of [tau]h is also addressed.