Asymptotically pointwise optimal procedures in sequential analysis

Abstract : After sequential analysis was developed by Wald in the forties [5], Arrow, Blackwell, and Girshick [1] considered the Bayes problem and proved the existence of Bayes solutions. The difficulties involved in computing explicitly the Bayes solutions led Wald [6] to introduce asymptotic sequential analysis in estimation. Asymptotic in his sense, as for all subsequent authors, refers to the limiting behavior of the optimal solution as the cost of observation tends to zero. Chernoff [2] investigated the asymptotic properties of sequential testing. The testing theory was developed further by Schwarz [4] and generalized by Kiefer and Sacks [3]. This paper approaches the asymptotic theory from a slightly different point of view.