Regression with Given Marginals

Abstract

We consider the class of regression functions $\mathscr{M}(F, G) = \{m(x) = E\lbrack Y\mid X = x\rbrack, (X, Y) \in \Pi(F, G)\}$ where $\Pi(F, G)$ denotes the set of random vectors with marginal distributions $F$ and $G$. A characterization of $\mathscr{M}(F, G)$ is given together with a representation for the projection operator it induces in an appropriate Hilbert space.

Locations

• The Annals of Statistics - View - PDF