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September, 1979 Monotone Regression and Covariance Structure
Gerald Shea
Ann. Statist. 7(5): 1121-1126 (September, 1979). DOI: 10.1214/aos/1176344794


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.


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Gerald Shea. "Monotone Regression and Covariance Structure." Ann. Statist. 7 (5) 1121 - 1126, September, 1979.


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

zbMATH: 0423.62039
MathSciNet: MR536513
Digital Object Identifier: 10.1214/aos/1176344794

Primary: 62H20
Secondary: 62H05

Keywords: Covariance , independence , monotone regression , Quadrant dependence , statistical diagnosis

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 5 • September, 1979
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