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2019

A simple measure of conditional dependence

Azadkia, Mona, Chatterjee, Sourav

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We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, based on an i.i.d.

sample.
The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in $[0,1]$, where the limit is $0$ if and only if $Y$ and $Z$ are conditionally independent given $X_1,\ldots,X_p$, and is $1$ if and only if $Y$ is equal to a measurable function of $Z$ given $X_1,\ldots,X_p$.
Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial $R^2$ statistic for measuring conditional dependence by regression.

A simple measure of conditional dependence · Around

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1906
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Chatterjee, S
Original
1909
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1954
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1994
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1995
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1996
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1996
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