Goodness‐of‐Fit Tests

Generally we test that Xi are iid with distribution F (or perhaps omf or pdf f) from a parametric family of distributions F versus a general alternative F ∈ G\F , where G is the set of all possible distributions (of the right dimension and continuous or discrete form). Thus we are testing H0 : F ∈ F versusHA : F ∈ G\F . This is a hypothesis test, but not of a parametric form. It is not easy to put this into a GLR form.