Studentization of the generalized covariance measure statistic

If the numerator of the generalized covariance measure statistic obeys a central limit theorem with variance $\mathbb{E}({\epsilon }^2{\xi }^2)$ and its empirical residual-product second moment converges in probability to the same positive quantity, the Slutsky theorem makes the studentized statistic converge in distribution to $N(0,1)$.