Construction of confidence absorbing sets using statistical methods

In this paper, the problem of constructing the confidence absorbing set is considered as follows: find the set of initial positions of a system for which at a terminal time instant a loss function will not exceed some fixed level with a given probability. The dependence of the system's state at the terminal time instant on its initial position is assumed to be a known random function. An approach to construct outer and inner approximations of the confidence absorbing set is proposed. In the first stage, deterministic inner and outer approximations are obtained. Then, these approximations are refined for a certain finite set of initial positions of the system using sample estimates. The sample size sufficient to construct the approximations is estimated. The latter estimate is improved for the case of a star-shaped loss function. An algorithm for constructing approximations of the confidence absorbing set in the two-dimensional case is developed. The resulting approximations are used in a production planning problem.