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October, 1976 Conditions on the Regression Function when Both Variables are Uniformly Distributed
R. A. Vitale, A. C. Pipkin
Ann. Probab. 4(5): 869-873 (October, 1976). DOI: 10.1214/aop/1176995992

Abstract

Consider the class of probability distributions on the unit square with uniform marginal distributions. The class of associated regression functions is characterized by integral inequalities or, equivalently, as forming the closed convex hull of 1-1, measure-preserving mappings of the unit interval onto itself.

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R. A. Vitale. A. C. Pipkin. "Conditions on the Regression Function when Both Variables are Uniformly Distributed." Ann. Probab. 4 (5) 869 - 873, October, 1976. https://doi.org/10.1214/aop/1176995992

Information

Published: October, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0343.62054
MathSciNet: MR414829
Digital Object Identifier: 10.1214/aop/1176995992

Subjects:
Primary: 62J05
Secondary: 28A65

Keywords: measure-preserving mapping , regression function

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 5 • October, 1976
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