A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

By Liangjun Su, Halbert White. 2008

223 citations recorded by the source corpus.

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y|x,z) and f(y|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n−1/2h−d/4. The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “104 Hilbert Space Embedding of Conditional Distributions There exist numerous tests for conditional dependency such as partial correlation tests (Baba et al. 2004), conditional densities based tests (Su and White 2008), and permutation-based tests (Tsamardinos and Borboudakis 2010).”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “For example, Su and White (2008) deﬁne the test statistic as some distance be-tween the estimated conditional densities p ( X | Y, Z ) and p ( X | Y ), and Su and White (2007) exploit the difference between the characteristic functions of these conditional densities.”
Testing Conditional Independence Via Empirical Likelihood (2014, methodology): “One can follow Su and White (2008) to establish the asymptotic validity of this bootstrap procedure.”
A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion (2014, methodology): “Testing procedures for Granger causality in the whole distribution in a time series context are developed only in Su and White (2007, 2008, 2012, 2014), Bouezmarni, Rombouts, and Taamouti (2012), and Taamouti, Bouezmarni, and El Ghouch (2014).”
Automated Machine Learning: Methods, Systems, Challenges (2019, unknown): “Another popular model for generating pairs is the post-non-linear (PNL) model [66]:”
Causality detection based on information-theoretic approaches in time series analysis (2007, background): “[23], or test for conditional independence based on Hellinger distances [223], also exist, however, their applications have been quite limited, so far.”
The conditional permutation test for independence while controlling for confounders (2018, background): “…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, 2008) and smoothed empirical likelihoods (Su and White, 2014).”
Search for Additive Nonlinear Time Series Causal Models (2008, background): “For example, Su and White (2007) propose a conditional independence test for stationary time series satisfying certain conditions, based on a weighted Hellinger distance between fX |Y Z(x;y,z) and fX |Z(x;z), where fX |Y Z(x;y,z) and fX |Z(x;z) are densities of the conditional distributions of X…”
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].”
Testing Conditional Independence via Rosenblatt Transforms (2009, background): “See Linton and Gozalo (1997), Delgado and González Manteiga (2001), Angrist and Kuersteiner (2004) and Su and White (2008), among others.”
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, methodology): “Wang and Hong [38] develop a new test based on characteristic functions, which achieves faster rates against certain local alternatives in comparison to the test developed by Su and White [32].”
Granger Causality and Dynamic Structural Systems (2010, methodology): “…consistent against arbitrary alternatives are readily available (e.g., Linton and Gozalo, 1997; Fernandes and Flores, 2001; Delgado and Gonzalez-Manteiga, 2001; and Su and White, 2007a, 2007b, 2008), but given the large number of covariates in most applications, these are often not practical.”
A Permutation-Based Kernel Conditional Independence Test (2014, methodology): “Some tests use this characterization to determine conditional independence by measuring the distance between estimates of these conditional densities (Su and White, 2008).”
Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis (2013, methodology): “Su and White [47] propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities.”
Strongly consistent nonparametric tests of conditional independence (2012, methodology): “Under density assumption Su and White (2008a, 2008b), used Hellinger metric and characteristic functions, respectively, relaxing the independence assumption on the sample.”