Goodness-of-fit tests for regression models

International audienceThe objective is to construct a tool to test the validity of a regression model. For this, we have studied some omnibus tests of goodness-of-fit. Our study focuses on the regression function in the regression model. These tests can be ``directional'' in that they are designed to detect departures from mainly one given assumption of the model (regression function, variance function or error) or global with the conditional distribution function. We have compared, through simulations, different nonparametric methods to test the validity of the model. Two methods are directional and one is global. The establishment of such statistical tests require nonparametric estimators and the use of wild bootstrap methods for the simulations