Statistical Analysis Stack Exchange
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Questions tagged [distance-covariance]

A measure of dependence between two random variables (or two random vectors of any dimension). Also called Brownian covariance.

Distance (also known as Brownian) covariance and correlation are measures of statistical dependence between two random variables (or two random vectors of any dimension), introduced by Gábor Székely in 2005. Distance covariance between $X$ and $Y$ is zero if and only if $X$ and $Y$ are independent. Sample distance covariance is computed via the matrices $A_{ij}=\|X_i-X_j\|$ and $B_{ij}=\|Y_i-Y_j\|$ of pairwise distances between all points in the sample.

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Understanding distance correlation computations

As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers: (x1, y1) (x2, y2) ... (xn, yn) we can use distance…
Roman
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When is distance covariance less appropriate than linear covariance?

I've just been introduced (vaguely) to brownian/distance covariance/correlation. It seems particularly useful in many non-linear situations, when testing for dependence. But it doesn't seem to be used very often, even though covariance/correlation…
naught101
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Distance correlation versus mutual information

I've worked with the mutual information for some time. But I found a very recent measure in the "correlation world" that can also be used to measure distribution independence, the so called "distance correlation" ( also termed Brownian correlation):…
dsign
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Is there an intuitive characterization of distance correlation?

I've been staring at the wikipedia page for distance correlation where it seems to be characterized by how it can be calculated. While I could do the calculations I struggle to get what distance correlation measures and why the the calculations look…
Rasmus Bååth
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Distance between independent observations of a categorical variable

I have a random variable $T$ that takes values in $\{ \text{blue}, \text{green}, \text{red} \}$, and a number of observations of $T$: |i |T | |:--|:-----| |1 |red | |2 |red | |3 |green | |4 |red | |5 |blue | |6 |blue | |7 |green…
shadowtalker
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What precisely is the interpretation of distance correlation?

The key feature of distance correlation is that if it is $0$ then two variables are independent. If the pearson correlation is zero, however, this does not imply independence. How would one interpret distance correlation?
proton
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Interpretable General Measure of Dependence

I am looking for an interpretable measure between two random variables $X$ and $Y$ which quantifies the dependence between the two but does not assume linearity. Essentially, I am looking for a nonlinear variant of the shared variance. The shared…
Julian Karch
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Explaining the difference between Pearson correlation and distance correlation

This question and its answer might highlight my naivete regarding Brownian/distance correlation. I'm using the difference between a matrix of distance correlations, as calculated by energy::dcor(), and absolute value Pearson correlations, as…
topherwhatever
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What is the distance correlation for Anscombe’s quartet?

Is the newer descriptive statistic (distance correlation) able to resolve these troubling four datasets (Anscombe’s quartet)?
Felipe G. Nievinski
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Methods for determining temporal covariance among many time series?

We are trying to quantify synchrony in water chemistry variation among several thousand sites. For each site we have a time-series of concentration. We'd like to quantify the overall temporal covariance (are concentrations going up and down at the…
benjabiker
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What conditions are needed for a differentiable random field?

I've been playing around with some random field models and noticed that the apparent differentiability seems to be related to the covariance function's behavior at 0. My initial guess was that if $\frac d {dx} C(x) = 0$, then a resulting random…
jjet
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Is the absolute value of distance covariance a metric?

I'm reasonably certain the absolute value of the distance covariance satisfies $d(x, y) \ge 0$ (non-negativity, or separation axiom) $d(x, y) = 0$ if and only if $x = y$ (identity of indiscernibles, or coincidence axiom) $d(x, y) = d(y,…
naught101
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multivariate classification r

I am analyzing a dataset with 5 factors(Y1,Y2,Y3,Y4,Y5). ID Y1 Y2 Y3 Y4 Y5 1 5 1 2 9 40 2 6 1 17 9 49 3 5 1 6 10 25 4 5 1 …
Ahir Bhairav Orai
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Does distance correlation work for count data?

I'm considering using partial distance correlation to test for conditional independence in multivariate count data. However, I haven't been able to find any good sources that discuss whether (partial) distance correlation works well for count data.…
Cameron Bieganek
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Why is distance covariance defined squared, while covariance is not?

I am dealing in a data science project with correlation analyses using pearson and distance correlation. While trying to understand the differences between them, I learned about the differences by reading Szekely's paper and finding this very good…
gehbiszumeis
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