Stability of Filtered Experiments

Summary

A family of probability measures on a filtered probability space is called a filtered experiment. It is shown that sequences of filtered experiments, which are obtained by rescaling a fixed filtered experiment, can only have weak limits satisfying an invariance property called stability. This property allows a simplified approach to the problem of determining the sample size needed for separating parameter points by critical functions. In case of independent, identically distributed observations, the result covers previous assertions obtained by the author, [3]. In general, the result covers the case of dependent observations. It can be explained, how so-called mixed-normal situations arise in the limit. As a by-product we show, how an increasing family of experiments can be represented by a filtered experiment.