Conditionally selective dependence of random variables on external factors (Q1283555)

Let \(X_1,\dots,X_n\) be a set of random variables and let \({\mathcal F}\) be a set of external factors affecting the joint distribution of these random variables. The author considers selective influence, stochastic interdependence, conditionally selective influence, and unconditional and conditional selectivity of \(X_1,\dots,X_n\). The main result of the paper is Theorem 3, which describes the structure of the joint distribution that is necessary and sufficient for \(X_1,\dots,X_n\) to be conditionally selectively influenced by some subsets of \({\mathcal F}\).