Abstract
An approach to simultaneous treatment of dependence and screening problems is presented. New characterizations of dependence of a random variable $X$ on a random vector $Y$ are obtained by functions $\nu_{X, Y}: (0, 1)\rightarrow \lbrack 0, 1\rbrack$ and $\mu_{X, Y} : (0, 1) \rightarrow \lbrack -1, 1\rbrack$ called respectively screening and monotonic dependence functions. These functions are shown to be appropriate measures of the intensity of connection and concordance of $X$ on $Y$, respectively. The interrelations of $\nu$ and $\mu$ and their relations to the multiple correlation ratio and the multiple correlation coefficient are demonstrated and illustrated by several examples.
Citation
T. Kowalczyk. A. Kowalski. A. Matuszewski. E. Pleszczynska. "Screening and Monotonic Dependence Functions in the Multivariate Case." Ann. Statist. 7 (3) 607 - 614, May, 1979. https://doi.org/10.1214/aos/1176344682
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