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A Nonparametric Hellinger Metric Test For Conditional Independence, Liangjun Su, Halbert White
A Nonparametric Hellinger Metric Test For Conditional Independence, Liangjun Su, Halbert White
Research Collection School Of Economics
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 …