4.7 Article

Testing Conditional Independence via Quantile Regression Based Partial Copulas

Journal

JOURNAL OF MACHINE LEARNING RESEARCH
Volume 22, Issue -, Pages -

Publisher

MICROTOME PUBL

Keywords

Conditional independence testing; nonparametric testing; partial copula; conditional distribution function; quantile regression

Funding

  1. VILLUM FONDEN [13358]

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This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. The resulting test is demonstrated to be sound under complicated data generating distributions and competitive to other state-of-the-art conditional independence tests, with superior power in cases with conditional variance heterogeneity of X and Y given Z.
The partial copula provides a method for describing the dependence between two random variables X and Y conditional on a third random vector Z in terms of nonparametric residuals U-1 and U-2. This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. We consider a test statistic based on generalized correlation between U-1 and U-2 and derive its large sample properties under consistency assumptions on the quantile regression procedure. We demonstrate through a simulation study that the resulting test is sound under complicated data generating distributions. Moreover, in the examples considered the test is competitive to other state-of-the-art conditional independence tests in terms of level and power, and it has superior power in cases with conditional variance heterogeneity of X and Y given Z.

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