Linear regression with statsmodels

Question

I am trying to fit a linear regression model implemented in statsmodels library. The distribution of the error term is a t-distribution with (sigma>0 and dof>2) as depicted below.

Is it possible to produce such a likelihood in statsmodels, making use of generic likelihood method?

Answer 1

This is a test and example case for GenericLikelihoodModel in statsmodels.

see https://www.statsmodels.org/dev/generated/statsmodels.miscmodels.tmodel.TLinearModel.html for the TLinearModel and the source code for how to implement generic maximum likelihood models.

Some examples are in the unit tests https://github.com/statsmodels/statsmodels/blob/master/statsmodels/miscmodels/tests/test_tmodel.py