I have some difficulties understanding the QMLE. Literature is a little bit short on QMLE, it only proove asymptotic normality but does not say much more. Is it true that if I want to estimate the parameters of a model with QMLE I first assume normality. If the data violate this condition the QMLE is may still be consistent (under certain conditions). So the difference between the MLE and the QMLE is that the QMLE can still be consitent even though the data is not normal?