Distance Covariance in Metric Spaces

By Ann. Probab. 2017

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “A related but different class of tests are distance-based “energy statistics” as introduced in parallel by Baringhaus and Franz [2004] and Sz´ekely and Rizzo [2004], and generalized to some kinds of metrics, denoted ρ , for a related independence testing problem, by Lyons [2013].”
On the Decreasing Power of Kernel and Distance Based Nonparametric Hypothesis Tests in High Dimensions (2014, methodology): “One can use other distance metrics instead of Euclidean norms to generalize the deﬁnition to metric spaces, see (Lyons 2013).”
Applications of distance correlation to time series (2016, methodology): “Further progress on this topic has been achieved in Sejdinovic et al. (2013) and Lyons (2013), who generalized correlation distance to a metric space.”
Demystifying MMD GANs (2018, background): “The energy distance (Székely & Rizzo, 2004; Lyons, 2013) is a measure of divergence between two probability measures, deﬁned as”
On the High Dimensional Power of a Linear-Time Two Sample Test under Mean-shift Alternatives (2015, background): “…by Székely & Rizzo (2004) is closely tied to the MMD - indeed it has the same form as the MMD with the Euclidean distance instead of a kernel; Lyons (2013) showed that one can also use other metrics instead of the Euclidean distance and Sejdinovic et al. (2013) showed that there is a close…”
Large-scale kernel methods for independence testing (2016, background): “We note that Lyons (2013) gives a proof to a similar theorem (Theorem 2.”
The exact equivalence of distance and kernel methods in hypothesis testing (2018, methodology): “Distance correlation is applicable to any metric choice, while the HilbertSchmidt independence criterion may use any kernel choice, and the consistency property still holds under proper conditions (Lyons 2013; Gretton et al. 2005).”
Statistical Dependence: Beyond Pearson’s ρ (2018, background): “See also Nguyen et al. (2020). A local Gaussian conditional distribution allows the introduction of a local Gaussian partial correlation, and density and conditional density estimation, as well as tests of conditional independence treated by Otneim and Tjøstheim (2017, 2018; 2019). Locally Gaussian ”
Testing mutual independence in high dimension via distance covariance (2016, background): “For example, when the p components have a natural ordering, which arises in time series analysis, testing for m-dependence is of particular interest (see Moon and Velasco (2013)).”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, methodology): “Moreover, the kernel corresponding to α = 1 is also the distance covariance kernel, which is very popular in statistics (see [103, 67]).”
Partial martingale difference correlation (2015, background): “…dependence of two random vectors X ∈ Rp and Y ∈ Rq, Székely, Rizzo and Bakirov [13] proposed distance covariance (dCov) and distance correlation (dCor), which have attracted a lot of attention lately; see related work by Sźekely and Rizzo [12], Li, Zhong and Zhu [7], Kong et al. [4], Lyons [8],…”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, background): “are then characteristic for the collection of probability distributions with finite second moments [64, 86].”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “5) or results from degenerate V-statistics (as used in (Lyons 2013, theor.”
On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests (2015, background): “and in fact also other metrics; Reference [40] explains the details for the closely related independence testing problem.”