Testing Conditional Independence via Quantile Regression Based Partial Copulas
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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 U1 and U2. 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 U1 and U2 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. © 2021 Lasse Petersen and Niels Richard Hansen.
Original language | English |
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Journal | Journal of Machine Learning Research |
Volume | 22 |
Pages (from-to) | 1-47 |
ISSN | 1533-7928 |
Publication status | Published - 2021 |
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