Strongly consistent nonparametric tests of conditional independence

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Joint Causal Inference from Multiple Contexts (2016, methodology): “Another example of a distribution-free and even strongly-consistent conditional independence test is proposed by Györfi and Walk (2012). In general, when using the p-value as a test statistic, one should choose the sample-size dependent threshold αN (where the p-value of the test result is used to d”
Minimax optimal conditional independence testing (2020, background): “In an interesting paper, Györfy and Walk [16], extend the independence testing results of Gretton and Györfi [15] to the CI case, and propose strongly consistent nonparametric tests.”
Energy statistics: A class of statistics based on distances (2013, background): “For other recent consistent tests of bivariate or multivariate independence see e.g. Feuerverger (1993), Gretton and Györfi (2010), and Gretton and Györfi (2012).”