Distance multivariance: new dependence measures for random vectors

DOI10.1214/18-AOS1764zbMath1467.62104arXiv1711.07775OpenAlexW2964719927MaRDI QIDQ2328059

Martin Keller-Ressel, Björn Böttcher, Rene L. Schilling

Publication date: 9 October 2019

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.07775

zbMATH Keywords

multivariancecharacteristic functionstochastic independenceGaussian random fieldnegative definite functiondependence measurestatistical test of independence

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Measures of association (correlation, canonical correlation, etc.) (62H20) Nonparametric tolerance and confidence regions (62G15) Characteristic functions; other transforms (60E10)

Related Items (14)

Detecting independence of random vectors: generalized distance covariance and Gaussian covariance ⋮ Generalization of the energy distance by Bernstein functions ⋮ Generalization of the HSIC and distance covariance using PDI kernels ⋮ Copula versions of distance multivariance and dHSIC via the distributional transform – a general approach to construct invariant dependence measures ⋮ Measuring linear correlation between random vectors ⋮ Quantifying directed dependence via dimension reduction ⋮ Rényi 100, quantitative and qualitative (in)dependence ⋮ A Szekely-Rizzo inequality for testing general copula homogeneity hypotheses ⋮ The distance standard deviation ⋮ A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models ⋮ multivariance ⋮ Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin ⋮ Statistical dependence: beyond Pearson's \(\rho\) ⋮ Distance multivariance: new dependence measures for random vectors

Uses Software

• R

Cites Work

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