Conditional distance correlation

Based on the sample version, we propose a test for conditional independence, which is proven to be more powerful than some recently developed tests through our numerical simulations. The advantage of our test is even greater when the relationship between the multivariate random variables given the third random variable cannot be expressed in a linear or monotonic function of one random variable versus the other. We also show that the sample measure is consistent and weakly convergent, and the test statistic is asymptotically normal.

By applying our test in a real data analysis, we are able to identify two conditionally associated gene expressions, which otherwise cannot be revealed. Thus, our measure of conditional dependence is not only an ideal concept, but also has important practical utility.