Using estimated parameters, the question arises which estimation method should be used. Usually this would be the maximum likelihood method, but e.g. for the normal distribution MLE has a large bias error on sigma. Using a moment fit or KS minimization instead has a large impact on the critical values, and also some impact on test power. If we need to decide for Student-T data with df = 2 via KS test whether the data could be normal or not, then a ML estimate based on H0 (data is normal, so using the standard deviation for scale) would give much larger KS distance, than a fit with minimum KS. In this case we should reject H0, which is often the case with MLE, because the sample standard deviation might be very large for T-2 data, but with KS minimization we may get still a too low KS to reject H0. In the Student-T case, a modified KS test with KS estimate instead of MLE, makes the KS test indeed slightly worse. However, in other cases, such a modified KS test leads to slightly better test power.
using estimated parameters the question arises which estimation method should be used usually this would be the maximum likelihood method but eg for the normal distribution mle has a large bias error on sigma using a moment fit or ks minimization instead has a large impact on the critical values and also some impact on test power if we need to decide for student-t data with df = 2 via ks test whether the data could be normal or not then a ml estimate based on h0 (data is normal so using the standard deviation for scale) would give much larger ks distance than a fit with minimum ks in this case we should reject h0 which is often the case with mle because the sample standard deviation might be very large for t-2 data but with ks minimization we may get still a too low ks to reject h0 in the student-t case a modified ks test with ks estimate instead of mle makes the ks test indeed slightly worse however in other cases such a modified ks test leads to slightly better test power