Properties of Decision Functions Defined by Bans*

Abstract

Random sequences over a fixed finite alphabet are considered. It is assumed that the sequence is generated by one of m probability distributions on the space of infinite sequences. For a probability measure on the space of infinite sequences a set of projections on a finite number of initial coordinates is considered. The ban of a measure in any projection is defined as a vector having zero probability in this projection.

The problem consists in the search for conditions under which the observations of random sequences on a segment of finite length allow to correctly define the true distribution with probability 1. In the paper, necessary and sufficient conditions are found under which there exists statistical decision determined by bans possessing specified properties. The existence of statistical decisions with specified properties makes them promising for applications in monitoring systems.