Open Access
May, 1979 Screening and Monotonic Dependence Functions in the Multivariate Case
T. Kowalczyk, A. Kowalski, A. Matuszewski, E. Pleszczynska
Ann. Statist. 7(3): 607-614 (May, 1979). DOI: 10.1214/aos/1176344682


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.


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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.


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

zbMATH: 0421.62042
MathSciNet: MR527496
Digital Object Identifier: 10.1214/aos/1176344682

Primary: 62G99
Secondary: 62H20 , 62H30

Keywords: measures of monotonic dependence , multiple correlation coefficient , regression functions , Screening , selection , truncation

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 3 • May, 1979
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