The invariant optimal sampling plan in a sequentially planned decision procedure

Abstract

We define the invariant sequentially planned decision procedure under a group of measurable transformations. By means of a previous reduction of the problem, we obtain the optimal invariant sequentially planned decision procedure that minimizes the risk function. First we find the solution for the horizon with a maximal number of stages, based on the present information; later, the general case is solved but the solution is based on the past information. Finally, we study the possibility of approximating the general case by a sequence of truncated problems with a maximal number of stages, obtaining a solution based on the present informatio