Is there a way to check the parabola assumption of the HESSE routine of Minuit? I see some differences between the errors of MINOS and HESSE but I am not sure if the differences are big enough to trust the covariance estimate of HESSE. The negative likelihood plotted as a function of one of the parameters also does not give a perfect parabola but again, I don’t know if the discrepancy is big enough.
The bast way I think is computing the Minos errors. This is like doing an efficient scan of the profile likelihood around the minimum. If you observe large differences then the parabola approximation is not valid. Further more, if you care close to a bound (lower or upper) then again the parabola approximation is not valid