Testing Functional Connection between Two Random Variables

Abstract

Two discrete random variables, ξ and η are considered. The goal is to decide whether $\eta$ is a function of ξ. A series of tests are performed, $(\xi _{i},\eta _{i}),1\,\leq \,i\,\leq \,m$, are independent experiences with the same distribution as $(\xi ,\eta )$. The hypothesis is declined if $\xi _{i} = \xi _{j},\eta _{i}\neq \eta _{j}$ holds for some $i\neq j$. A condition is given on the character of convergence of the joint distribution of ξ and η ensuring the rejection of the hypothesis with a given limiting probability p.

Mathematics Subject Classification (2010): 60F99