Björn Böttcher
2020-May-04 09:04 UTC
[R] [R-pkgs] multivariance: Measuring Multivariate Dependence Using Distance Multivariance
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 Bj?rn B?ttcher References: [1] B. B?ttcher, 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. B?ttcher, 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. B?ttcher, 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. B?ttcher, On complex Gaussian random fields, Gaussian quadratic forms and sample distance multivariance. Preprint. https://arxiv.org/abs/1808.07280 [5] B. B?ttcher, 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. B?ttcher, 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. Bj?rn B?ttcher TU Dresden Institut f?r 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/ _______________________________________________ R-packages mailing list R-packages at r-project.org https://stat.ethz.ch/mailman/listinfo/r-packages