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July, 1978 Monotone Dependence
George Kimeldorf, Allan R. Sampson
Ann. Statist. 6(4): 895-903 (July, 1978). DOI: 10.1214/aos/1176344262


Random variables $X$ and $Y$ are mutually completely dependent if there exists a one-to-one function $g$ for which $P\lbrack Y = g(X)\rbrack = 1.$ An example is presented of a pair of random variables which are mutually completely dependent, but "almost" independent. This example motivates considering a new concept of dependence, called monotone dependence, in which $g$ above is now required to be monotone. Finally, this monotone dependence concept leads to defining and studying the properties of a new numerical measure of statistical association between random variables $X$ and $Y$ defined by $\sup \{\operatorname{corr} \lbrack f(X), g(Y)\rbrack\},$ where the $\sup$ is taken over all pairs of suitable monotone functions $f$ and $g.$


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George Kimeldorf. Allan R. Sampson. "Monotone Dependence." Ann. Statist. 6 (4) 895 - 903, July, 1978.


Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62059
MathSciNet: MR491562
Digital Object Identifier: 10.1214/aos/1176344262

Primary: 62H20
Secondary: 62H05

Keywords: association , Correlation , monotone correlation , monotone dependence , sup correlation

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • July, 1978
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