= Studentization of the generalized covariance measure statistic
Suppose the scaled mean residual product $\sqrt n\,\overline R$ in the <generalized covariance measure statistic> converges in distribution to $N(0,v)$, with $v>0$, and its empirical <variance> $s_R^2=n^{-1}\sum_iR_i^2-\overline R^2$ converges in <probability> to $v$. Then the <Slutsky theorem> gives $\sqrt n\,\overline R/s_R\Rightarrow N(0,1)$. It is the square root of the <variance> estimate that belongs in the denominator. Under the null and suitable regression conditions, $v=\mathbb E[\varepsilon^2\xi^2]$ for the two true regression residuals. This is a calibration argument; it does not remove the conditions needed for the numerator <limit> or <variance> consistency.<The Hardness of Conditional Independence Testing and the Generalised Covariance Measure by Rajen D. Shah and Jonas Peters>[§3.1]{ref}
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