(2018) proved that without further assumptions, H 0 will be rejected with a significance level of α if: where F n , G m are the empirical CDFs with n and m samples, respectively, is the violation level, Φ −1 is the inverse CDF of a normal distribution andσ n,m is the estimated variance of the value where is computed using samples X * n , Y * m from the empirical distributions F n and G m .
we consider this ambiguity an inherent limitation of the COS method.