Testing conditional independence using maximal nonlinear conditional correlation

Details Testing conditional independence using maximal nonlinear conditional correlation Testing conditional independence using maximal nonlinear conditional correlation

2010-10-19

arxiv.org/abs/1010.3843v1

Annals of Statistics 2010, Vol. 38, No. 4, 2047-2091

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS770 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS770

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

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