Testing conditional independence using maximal nonlinear conditional correlation

By Tzee-Ming Huang. 2010

81 citations recorded by the source corpus.

In this paper, the maximal nonlinear conditional correlation of two random vectors X and Y given another random vector Z, denoted by ρ 1 (X, Y|Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When Z is continuous, a test for testing the conditional independence of X and Y given Z is constructed based on the estimator of a weighted average of the form Σ nZ k=1 f Z (z k )ρ 2 1 (X, Y|Z = z k ) , where f Z is the probability density function of Z and the z k 's are some points in the range of Z. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “Meth-ods in the second category, such as Margaritis (2005) and Huang (2010), discretize the conditioning set Z to a set of bins, and transform CI to the unconditional one in each bin.”
Minimax optimal conditional independence testing (2020, methodology): “Huang [18] proposes a nonparametric CI test using the so called maximal nonlinear conditional correlation.”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, background): “…2014) (on conditional characteristic functions, conditional probability density functions, and smoothed empirical likelihood ratios, respectively); Huang (2010) (on maximal nonlinear conditional correlation); Fukumizu et al. (2008), Zhang et al. (2011), Doran et al. (2014), and Strobl et al.…”
Approximate Kernel-Based Conditional Independence Tests for Fast Non-Parametric Causal Discovery (2017, unknown): “One strategy involves discretizing continuous conditioning variables Z as Z̆ in some optimal fashion and assessing unconditional independence ∀Z̆ = ̆ z [6, 7].”