Sequential Estimation in the Uniform Density.

The main problem to be solved here may be described as follows: Let X[sub 1], X[sub 2], ... be independent random variables, each with density f[sub theta](x) = 1/theta over (0, theta) and zero elsewhere. It is desired to estimate the unknown parameter 0 by an interval of length of most d units and with confidence at least 1 - alpha, for some specified d > 0 and alpha in (0, 1). An exact solution and an asymptotic theory for a sequential procedure are given in Sections 1 and 2, respectively. The procedure proposed in this article satisfies an admissibility criterion which may be stated in terms of the maximum possible number of observations or, alternatively, the expected number of observations. [ABSTRACT FROM AUTHOR]