讲座 | Conditional dependence for multivariate random variables
主讲人: 王学钦 教授, 中山大学
时间: 2013年三月27日（星期三），下午2:30
地点: F203
摘要:
Multivariate random variables are conditionally independent given a certain random variable if and only if their partial correlation is zero assuming that all involved random variables are multivariate Gaussian. However, sharing the same drawback with Pearson's correlation, the partial correlation is zero does not imply that random vectors are conditionally independent in general cases. Motivated by recently developed work of distance correlation, we introduce a measure of conditional dependence, conditional distance covariance(CDCov), which is zero if and only if random vectors are conditionally independent. When the CDCov is normalized, one get the conditional distance correlation(CDCor). Two CDCov's sample versions, called sample conditional distance covariances(SCDCov) is derived and represented as a V or U-process with random kernels. The SCDCov are consistent and weakly convergent. A conditional distance independence test(CDIT) statistic is naturally introduced to detect the conditional independence between multivariate variables and its limit distribution is a mixture of $\chi^2$ distributions. Numerical results also demonstrate that our test surpasses others, especially when the alternative hypothesis is that there is nonlinear and non-monotonic conditional dependence.