DISTRIBUTION FREE TESTS OF INDEPENDENCE BASED ON THE SAMPLE DISTRIBUTION FUNCTION

By J. Blum, J. Kiefer, M. Rosenblatt. 1961

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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).”
On Brownian Distance Covariance and High Dimensional Data (2009, neutral): “See, for example, Blomqvist [3], Blum, Kiefer, and Rosenblatt [4], or methods outlined in Hollander and Wolfe [16] and Anderson [1].”
On quadratic functionals of the Brownian sheet and related processes (2006, background): “[3] Blum, J. R., Kiefer, J. and Rosenblatt, M. (1961).”
A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE (2008, methodology): “There are many nonparametric tests of independence for continuous random variables, starting with Hoeffding (1948), including empirical distribution-based methods such as Blum et al. (1961) or Skaug and Tjostheim (1993), smoothing-based methods like Rosenblatt (1975), Robinson (1991), and Hong and”
An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, unknown): “Skaug and Tjøstheim (1993) extended the work by Blum et al. (1961) and considered the asymptotic behavior of the Cramer-von Mises type statistic (27) at lag j , under ergodicity of { X t } .”
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).”
Strongly consistent nonparametric tests of conditional independence (2012, background): “For d = d′ = 1, an early nonparametric test for independence, due to Hoeffding (1948), Blum et al. (1961), De Wet (1980), Cotterill and Csörgő (1985), is based on the notion of differences between the joint distribution function and the product of the marginals.”
A consistent modification of a test for independence based on the empirical characteristic function (1998, background): “3. Then each random variable Fk(Xk) has the uniform distribution on tile interval [0, 1 ] and hence the test based on the statistic T~ (F) is distribution free.”
A New Coefficient of Correlation (2019, background): “ls to address this deciency of the classical coecients [23], such as the maximal correlation coecient [5, 15, 21, 33], various coecients based on joint cumulative distribution functions and ranks [3, 4, 8, 9, 11, 14, 18, 22, 30, 32, 35, 36, 46{49], kernel-based methods [16, 17, 31, 40, 51], informat”
Copula-Based Measures of Multivariate Association (2010, background): “[6], Genest and Rémillard [40] as well as Genest et al.”
Conditionally independent private information in OCS wildcat auctions (2000, methodology): “(1999) through a Blum et al. (1961) nonparametric test of independence.”
On boosting the power of Chatterjee’s rank correlation (2021, background): “For the sake of testing consistency, Hoeffding (1948), Blum et al. (1961), Yanagimoto (1970), and Bergsma and Dassios (2014) have proposed variants ∗Department of Statistics, University of Washington, Seattle, WA 98195, USA; e-mail: zxlin@uw.edu †Department of Statistics, University of Washington,…”
A multivariate version of Hoeffding's Phi-Square (2010, unknown): “[3].”