On the uniqueness of distance covariance

By G'abor J. Sz'ekely, Maria L. Rizzo. 2012

71 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

The affinely invariant distance correlation (2012, background): “Computer code for calculating these sample versions is available in an R package by Rizzo and Székely [17].”
Energy statistics: A class of statistics based on distances (2013, background): “One can show that if two weighted L2 distances of the type (3.1) are equal for all characteristic functions f̂ and ĝ , then the (continuous) weight functions are also equal (for proof of a similar claim see Székely and Rizzo, 2012).”
Independent Component Analysis via Distance Covariance (2013, methodology): “That is, each component-wise Finally, we deﬁne a test statistic for mutual independence as (5) For d = 2, U n ( S ) is asymptotically distribution free and its asymptotic distribution can be derived from Theorem 5 of Sz´ekely and Rizzo (2009) and the Glivenko-Cantelli theorem.”
An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, unknown): “In addition, Wang et al. (2015) derive two consistent, ready-to-use sample measures for the conditional distance covariance, which do not involve integration of the empirical characteristic functions.”
Multivariate nonparametric test of independence (2017, methodology): “In the paper [29] even statements about uniqueness of those non-integrable weights have been derived under requirements for “rigid motion invariance and scale invariance” (see, e.”
Partial Distance Correlation with Methods for Dissimilarities (2013, unknown): “On the weight function applied, see also Feuerverger [5] and Székely and Rizzo [31].”
Fast Computing for Distance Covariance (2014, methodology): “, life science (Kong, Klein, Klein and Wahba 2012) and variable selection (Li, Zhong and Zhu 2012), and has been analyzed (Székely and Rizzo 2012; Lyons 2013), extended (Székely and Rizzo 2009; Székely and Rizzo To appear) in various aspects.”