The Penalty for Assuming that a Monotone Regression is Linear
Fairley, David ; Pearl, Dennis K. ; Verducci, Joseph S.
Ann. Statist., Tome 15 (1987) no. 1, p. 443-448 / Harvested from Project Euclid
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 $\operatorname{Corr}\lbrack Y, G^{-1}(F(X))\rbrack$.
Publié le : 1987-03-14
Classification:  Fixed margins,  inequalities,  intrinsic variation,  isotonic regression,  monotone regression,  62J02,  62E99,  62J05
@article{1176350279,
     author = {Fairley, David and Pearl, Dennis K. and Verducci, Joseph S.},
     title = {The Penalty for Assuming that a Monotone Regression is Linear},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 443-448},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350279}
}
Fairley, David; Pearl, Dennis K.; Verducci, Joseph S. The Penalty for Assuming that a Monotone Regression is Linear. Ann. Statist., Tome 15 (1987) no. 1, pp.  443-448. http://gdmltest.u-ga.fr/item/1176350279/