Mathematically: I have M vector showing the raw measurement. I get the reduced dataset as D=VT where T is non-blockdiagonal and non square matrix. How to fit D with a function f(p) to get reilable values and errors of the fitting p parameters.

My particular problem is fitting of Small Angle Scattering data:

The very simplified problem is that I have to divide the intensities I(q) by the transmission (which is also a statistical variable). A bit less simplified thus more problematic (and show the real problem) is that I want to extract the scattering of the container (divided also by it's transmission). This extraction increases the correlation between the statistical errors and this correlation is depending on the q-value. This correlation is sometimes resulted in reduced chisquare much below 1 giving untrustworthy values and the errors of them for the fitting parameters.