Monotone Regression and Covariance Structure

Shea, Gerald

Ann. Statist., Tome 7 (1979) no. 1, p. 1121-1126 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1979-09-14
Classification:  Covariance,  independence,  monotone regression,  quadrant dependence,  statistical diagnosis,  62H20,  62H05