A sequential procedure for estimating the mean of a normal distribution is proposed. The procedure is shown to have a negative regret at the origin and the same regret as the usual procedure at the other point asymptotically.
"A Sequential Procedure with Asymptotically Negative Regret for Estimating a Normal Mean." Ann. Statist. 20 (1) 562 - 569, March, 1992. https://doi.org/10.1214/aos/1176348540