Stoppping rules and ordered families of distributions

Abstract : There are good reasons for using sequential methods in some statistical decision problems, but a stopping rule that is helpful for deciding whether theta0 or theta0 may not be so good for estimating theta. This paper considers the construction of confidence bounds on a real parameter and investigates the relation between the ordering of boundary points that are accessible under the stopping rule and the natural ordering of the parameter space. Keywords: Confidence intervals; Monotone likelihood ratios; Stochastic ordering; Sequential decisions.