Abstract
The monotone regression of a variable $X$ on another variable $Y$ is of particular interest when $Y$ cannot be directly observed. The correlation of $X$ and $Y$ can be tested if at least high and low values of $Y$ can be recognized. If all the components of a random vector have monotone regression on a variable $Y$, and if they are all uncorrelated given $Y$, then an inequality due to Chebyshev shows that marginal zero covariances imply that all but at most one of the components are uncorrelated with $Y$. Cases are examined where marginal uncorrelatedness of attributes implies their independence. Applications to contaminated experiments and to discriminant analysis are noted.
Citation
Gerald Shea. "Monotone Regression and Covariance Structure." Ann. Statist. 7 (5) 1121 - 1126, September, 1979. https://doi.org/10.1214/aos/1176344794
Information