A consistent multivariate test of association based on ranks of distances

By Ruth Heller, Yair Heller, Malka Gorfine. 2012

272 citations recorded by the source corpus.

We consider the problem of detecting associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and consistent against all alternatives. The test has a simple form, is easy to implement, and has good power. Copyright 2013, Oxford University Press.

Subfields: Statistics and Probability

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Citations in the corpus

A low variance consistent test of relative dependency (2014, background): “, 2009; Gunn & Kandola, 2002), rankings (Heller et al., 2013), and space partitioning approaches (Gretton & Gyorfi, 2010; Reshef et al.”
Testing mutual independence in high dimension via distance covariance (2016, background): “Additionally, it is possible to combine the idea of aggregation with other tests that have been developed for independence of two univariate random variables (see, for example, Heller et al. (2013, 2016)) and form a test for pairwise independence.”
A New Coefficient of Correlation (2019, methodology): “…1959; Schweizer and Wolff 1981; Dette, Siburg, and Stoimenov 2013; Lopez-Paz, Hennig, and Schölkopf 2013; Zhang 2019), and coefficients based on pairwise distances (Friedman and Rafsky 1983; Székely, Rizzo, and Bakirov 2007; Székely and Rizzo 2009; Heller, Heller, and Gorfine 2013; Lyons 2013).”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, background): “, [81, 15, 86, 38, 103, 102, 41, 106, 47, 76, 82, 67, 53, 88, 61, 14, 10] and the references therein, however none of them satisfy (II).”
The affinely invariant distance correlation (2012, methodology): “nce increases when the transition is made to the aﬃnely invariant distance correlation. Alternative multivariate tests for independence based on distances have recently been proposed by Heller et al. [7] and Sz´ekely and Rizzo [22]. Aﬃnely invariant distance correlation 7 3. The aﬃnely invariant dis”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “[63] Heller, R.”
Equitability, mutual information, and the maximal information coefficient (2013, background): “Gorﬁne et al. [29] also recommend a diﬀerent statistic, HHG [31].”
Conditional quantile screening in ultrahigh-dimensional heterogeneous data (2015, background): “…is the constant in Condition 6 below. at U niversity of H ong K ong on February 24, 2015 http://biom et.oxfordjournals.org/ D ow nloaded from In fact, hk(y, t) = −cov{I (Y y), I (Zk < t)}, which is also the basis for the statistic used in Heller et al. (2013) to test independence of two variables.”
Multivariate nonparametric test of independence (2017, methodology): “However, in the comparison in [15], also some lack of sufficient power of dCov for small sample sizes such as n = 50 has been demonstrated, whereby HHG has shown much better power at these sample sizes.”