Testing conditional independence using maximal nonlinear conditional correlation


In this paper, the maximal nonlinear conditional correlation of two random vectors XX and YY given another random vector ZZ, denoted by ρ1(X,Y∣Z)\rho_1(X,Y|Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When ZZ is continuous, a test for testing the conditional independence of XX and YY given ZZ is constructed based on the estimator of a weighted average of the form βˆ‘k=1nZfZ(zk)ρ12(X,Y∣Z=zk)\sum_{k=1}^{n_Z}f_Z(z_k)\rho^2_1(X,Y|Z=z_k), where fZf_Z is the probability density function of ZZ and the zkz_k's are some points in the range of ZZ. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.Comment: Published in at the Annals of Statistics ( by the Institute of Mathematical Statistics (

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    Last time updated on 03/01/2020