Testing Conditional Independence Via Empirical Likelihood

By Liangjun Su, Halbert White. 2014

84 citations recorded by the source corpus.

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/5a0112b0399b3b46ac28c1738035854ae3036011

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Citations in the corpus

The conditional permutation test (2018, background): “There is also a large literature on extending measures of marginal independence to the conditional setting, including partial distance covariance [24]; conditional mutual information [15]; characteristic functions [21]; Hellinger distances [22]; and smoothed empirical likelihoods [23].”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, background): “…made to provide nonparametric solutions, and notable examples include Linton and Gozalo (1996) (on conditional cumulative distribution functions); Su and White (2007, 2008, 2014) (on conditional characteristic functions, conditional probability density functions, and smoothed empirical…”
Minimax optimal conditional independence testing (2020, background): “In the work [34] the authors propose an empirical likelihood based approach to CI testing.”
The conditional permutation test for independence while controlling for confounders (2018, background): “There is also a large literature on extending measures of marginal independence to the conditional setting, including partial distance covariance (Székely and Rizzo, 2014), conditional mutual information (Runge, 2018), characteristic functions (Su and White, 2007), Hellinger distances (Su and White,”