[R] [R-pkgs] multivariance: Measuring Multivariate Dependence Using Distance Multivariance

[Björn Böttcher]

Dear R-users and developers,

based on a recent series of of papers [1-6] the package 'multivariance' 
(available on CRAN; latest version 2.3.0, 2020-04-23) was developed.
It provides in particular:

+ *fast global tests of independence* for an arbitrary number of 
variables of arbitrary dimensions

+ a detection and visualization algorithm for *higher order dependence 
structures*

+ estimators for multivariate dependence measures which *characterize 
independence*, i.e. the population version is 0 if and only if the 
variables are independent (in contrast to the standard correlation 'cor')

As a side remark, some food for thought: Note that in [3] it is referred 
to over 350 datasets from more than 150 R-packages, which all feature 
some statistical significant higher order dependencies. Some are 
probably artefacts, but in any case it is likely that these have been 
unnoticed and undiscussed so far. Moreover, since it was purely a brute 
force study, this might provide starting points for plenty of research 
by the corresponding field specialists.

Comments and questions on 'multivariance' and the underlying theory are 
welcome.

Best wishes

Björn Böttcher


References:

[1] B. Böttcher, M. Keller-Ressel, R.L. Schilling, Detecting 
independence of random vectors: generalized distance covariance and 
Gaussian covariance.
Modern Stochastics: Theory and Applications, Vol. 5, No. 3 (2018) 353-383.
https://www.vmsta.org/journal/VMSTA/article/127/info

[2] B. Böttcher, M. Keller-Ressel, R.L. Schilling, Distance 
multivariance: New dependence measures for random vectors.
The Annals of Statistics, Vol. 47, No. 5 (2019) 2757-2789.
https://projecteuclid.org/euclid.aos/1564797863

[3] B. Böttcher, Dependence and Dependence Structures: Estimation and 
Visualization using the Unifying Concept of Distance Multivariance.
Open Statistics, Vol. 1, No. 1 (2020) 1-46.
https://doi.org/10.1515/stat-2020-0001

[4] G. Berschneider, B. Böttcher, On complex Gaussian random fields, 
Gaussian quadratic forms and sample distance multivariance. Preprint.
https://arxiv.org/abs/1808.07280

[5] B. Böttcher, Copula versions of distance multivariance and dHSIC via 
the distributional transform -- a general approach to construct 
invariant dependence measures.
Statistics, (2020) 1-18.
https://doi.org/10.1080/02331888.2020.1748029

[6] B. Böttcher, Notes on the interpretation of dependence measures -- 
Pearson's correlation, distance correlation, distance multicorrelations 
and their copula versions. Preprint.
https://arxiv.org/abs/2004.07649


-- 
Dr. Björn Böttcher
TU Dresden
Institut für Math. Stochastik
D-01062 Dresden, Germany
Phone: +49 (0) 351 463 32423
Fax:   +49 (0) 351 463 37251
Web:   http://www.math.tu-dresden.de/~boettch/

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