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.
Citation
Richard A. Vitale. "Regression with Given Marginals." Ann. Statist. 7 (3) 653 - 658, May, 1979. https://doi.org/10.1214/aos/1176344685
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