Distance-based and RKHS-based dependence metrics in high dimension

DOI10.1214/19-AOS1934zbMath1462.62279arXiv1902.03291MaRDI QIDQ1996774

Changbo Zhu, Shun Yao, Xianyang Zhang, Xiao-Feng Shao

Publication date: 26 February 2021

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

Full work available at URL: https://arxiv.org/abs/1902.03291

zbMATH Keywords

high dimensionalitydistance covarianceindependence testreproducing kernel Hilbert space (RKHS)Hilbert-Schmidt independence criterion\(\mathcal{U}\)-statistics

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Applications of statistics to environmental and related topics (62P12) Seismology (including tsunami modeling), earthquakes (86A15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (11)

Distance covariance for random fields ⋮ Marginal Distance and Hilbert-Schmidt Covariances-Based Independence Tests for Multivariate Functional Data ⋮ Testing for independence of high-dimensional variables: \(\rho V\)-coefficient based approach ⋮ Eigenvalue Distribution of a High-Dimensional Distance Covariance Matrix With Application ⋮ Generalization of the HSIC and distance covariance using PDI kernels ⋮ Asymptotic normality of Gini correlation in high dimension with applications to the \(K\)-sample problem ⋮ Rank-based indices for testing independence between two high-dimensional vectors ⋮ Independence tests with random subspace of two random vectors in high dimension ⋮ Interpoint distance based two sample tests in high dimension ⋮ Asymptotic distributions of high-dimensional distance correlation inference ⋮ A new framework for distance and kernel-based metrics in high dimensions

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