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March, 1987 The Penalty for Assuming that a Monotone Regression is Linear
David Fairley, Dennis K. Pearl, Joseph S. Verducci
Ann. Statist. 15(1): 443-448 (March, 1987). DOI: 10.1214/aos/1176350279

Abstract

For jointly distributed random variables $(X, Y)$ having marginal distributions $F$ and $G$ with finite second moments and $F$ continuous, the proportion of $\operatorname{Var}(Y)$ explained by linear regression is $\lbrack\operatorname{Corr}(X, Y)\rbrack^2$ while the proportion explained by $E(Y \mid X)$ can be arbitrarily near 1. However, if the true regression, $E(Y\mid X)$, is monotone, then the proportion of $\operatorname{Var}(Y)$ it explains is at most $\operatorname{Corr}\lbrack Y, G^{-1}(F(X))\rbrack$.

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David Fairley. Dennis K. Pearl. Joseph S. Verducci. "The Penalty for Assuming that a Monotone Regression is Linear." Ann. Statist. 15 (1) 443 - 448, March, 1987. https://doi.org/10.1214/aos/1176350279

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0613.62090
MathSciNet: MR885750
Digital Object Identifier: 10.1214/aos/1176350279

Subjects:
Primary: 62J02
Secondary: 62E99, 62J05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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