A non-parametric test of independence ∗

By J. E. García, V. González-López. 2011

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, background): “For example, Hoeffding [27] introduces a rank-based test in the case of univariate random variables and proves that it maintains uniformly asymptotic level and has asymptotic power against each fixed alternative.”
Invariant Causal Prediction for Nonlinear Models (2017, background): “There has been some progress towards nonparametric independence tests (Bergsma and Dassios, 2014; Hoeﬀding, 1948; Blum et al., 1961; R´enyi, 1959; Sz´ekely et al., 2007; Zhang et al., 2011).”
A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing (2013, unknown): “,Xn (Rüschendorf, 1976; Deheuvels, 1981), frequently defined as the empirical c.”
Equitability, mutual information, and the maximal information coefficient (2013, methodology): “dCor and Hoeffding’s D (20) performed similarly to one another, exhibiting nearly the same power as R(2) on the linear relationship and retaining substantial power on all but the checkerboard relationship.”
On the power of Chatterjee’s rank correlation (2020, methodology): “…if the pair is independent (Theorem 1.1 in Chatterjee, 2020); (ii) for F ∈ F c, D ≥ 0; for F ∈ FD, D = 0 if and only if the pair is independent (Theorem 3.1 in Hoeffding, 1948, Proposition 3 in Yanagimoto, 1970); (iii) for F ∈ F c, R ≥ 0 with equality if and only if the pair is independent (page…”
Large-Sample Theory for the Bergsma-Dassios Sign Covariance (2016, background): “see Hoeffding (1948). When (X, Y ) has a continuous joint distribution, it is readily seen that D = 0 if and only if X ⊥⊥ Y .”
Modeling Multivariate Distributions with Continuous Margins Using the copula R Package (2010, methodology): “The test of multivariate independence of Deheuvels (1981b) can be extended to test randomness as suggested by Genest and R´emillard (2004) (see also Ghoudi et al. 2001).”
FAST LARGE-SAMPLE GOODNESS-OF-FIT TESTS FOR COPULAS (2011, unknown): “…well according to recent large scale simulations (Genest, Rémillard, and Beaudoin (2009), Berg (2009)) is based on the empirical copula (Deheuvels (1981)) of the data (X1, Y1), . . . , (Xn, Yn), defined as Cn(u, v) = 1 n n∑ i=1 1(Ui,n ≤ u, Vi,n ≤ v), u, v ∈ [0, 1], (1.1) where the…”
A consistent test of independence based on a sign covariance related to Kendall's tau (2010, methodology): “Hoeffding’s [11] coefficient for measuring deviation from independence for a bivariate distribution function is given by (2) (see also Blum, Kiefer and Rosenblatt [4], Hollander and Wolfe [12] and Wilding and Mudholkar [27]).”
Large‐sample tests of extreme‐value dependence for multivariate copulas (2011, methodology): “payment and allocated loss adjustment expense data studied in Frees and Valdez (1998). These consist of 1466 general liability claims randomly chosen from late settlement lags (among the initial 1500 claims, 34 claims for which the policy limit was reached were ignored).”
Nonparametric independence testing via mutual information (2017, unknown): “Hoeﬀding’s test of independence (Hoeﬀding, 1948) is able to detect a wider class of departures from independence and is distribution-free under the null hypothesis but, as with these other classical methods, was only designed for univariate variables.”
High-dimensional consistent independence testing with maxima of rank correlations (2018, methodology): “For any pair of random variables, the correlation measure EhD ≥ 0 (Hoeffding, 1948, p. 547). Furthermore, it has been proven that, once the pair is absolutely continuous in R2, the correlation measure EhD = 0 if and only if the pair is independent (Hoeffding, 1948; Yanagimoto, 1970). This property, ”
Testing independence in high dimensions with sums of rank correlations (2015, methodology): “When the joint distribution of (X(p),X(q)) has continuous joint and marginal densities, the expectation E [ hD ( R(pq)i,1 , . . . ,R (pq) i,5 )] is zero if and only if X(p) and X(q) are independent [Hoeffding (1948a), Theorem 3.1].”
On boosting the power of Chatterjee’s rank correlation (2021, methodology): “Using Hoeffding’s inequality, for any > 0 and x > 0, P ( Gξ±(x)−GB(x) > ) ≤ exp(−2B 2).”