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


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.


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Richard A. Vitale. "Regression with Given Marginals." Ann. Statist. 7 (3) 653 - 658, May, 1979.


Published: May, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0401.62053
MathSciNet: MR527499
Digital Object Identifier: 10.1214/aos/1176344685

Primary: 62J05
Secondary: 28A65 , 46C10 , 60G25

Keywords: convex minorant , isotonic regression , nonlinear prediction , rearrangement of a function , regression

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 3 • May, 1979
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