  We propose an empirical likelihood test that is able to test the goodness of
fit of a class of parametric and semi-parametric multiresponse regression
models. The class includes as special cases fully parametric models;
semi-parametric models, like the multiindex and the partially linear models;
and models with shape constraints. Another feature of the test is that it
allows both the response variable and the covariate be multivariate, which
means that multiple regression curves can be tested simultaneously. The test
also allows the presence of infinite-dimensional nuisance functions in the
model to be tested. It is shown that the empirical likelihood test statistic is
asymptotically normally distributed under certain mild conditions and permits a
wild bootstrap calibration. Despite the large size of the class of models to be
considered, the empirical likelihood test enjoys good power properties against
departures from a hypothesized model within the class.
