Testing Conditional Independence via Quantile Regression Based Partial Copulas
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Testing Conditional Independence via Quantile Regression Based Partial Copulas. / Petersen, Lasse; Hansen, Niels Richard.
In: Journal of Machine Learning Research, Vol. 22, 2021, p. 1-47.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Testing Conditional Independence via Quantile Regression Based Partial Copulas
AU - Petersen, Lasse
AU - Hansen, Niels Richard
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
M3 - Journal article
VL - 22
SP - 1
EP - 47
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
SN - 1533-7928
ER -
ID: 260351057