<firstname.lastname@example.org> wrote in message news:email@example.com... The question arises: what determines the correct likelihood function ? a.) the distributuion of G - the measured values ? b.) the distribution of the residuals g(i)-G(i) ?
Neither. You need to start from the conditional distrbution of the observations given the explanatory variables.... don't think intially about "residuals". The usual advice would be to move away from normal-theory-based linear models to the sort of stuff described in http://en.wikipedia.org/wiki/Generalized_linear_model . You will Generalized Linear Models available in most statistical packages and they will be described in many statistical text books that go beyond the most basic stuff.