This paper is concerned with sequential minimax estimation of the parameter $\theta(0 < \theta < \infty)$ of the density function (3.1) when the observations are independently and identically distributed with this density, each observation costs the same amount $c > 0$, and the weight function is as given in Section 2. A procedure requiring a fixed sample size is shown to be a minimax solution for this problem.
"Sequential Minimax Estimation for the Rectangular Distribution with Unknown Range." Ann. Math. Statist. 23 (4) 586 - 593, December, 1952. https://doi.org/10.1214/aoms/1177729337