Discussion on: "An updated review of Goodness-of-Fit tests for regression models" (by W. Gonzales-Manteiga and R.M. Crujeiras)

First of all I would like to congratulate the authors for writing this very interesting, timely and thorough review paper. It is an almost impossible task to review the very extensive literature on smoothing based goodness-of-fit tests in regression in one single paper. Nevertheless, the paper contains a very rich collection of the contributions over the last 10-20 years, not only about goodness-of-fit tests for the regression function, but also regarding the variance function, the error distribution, the case of incomplete or dependent data, and much more. A comprehensive book on goodness-of-fit tests in regression using smoothing based approaches is somewhat missing in the literature, and I hope that the authors will use this paper as a starting point for a more extensive book on this topic. In this discussion I would like to comment on three issues, which the authors did not consider in their review : (1) Goodness-of-fit tests for the coefficient of variation; (2) tests for the independence between the error term and the covariates; and (3) some open questions and comments.