Testing procedures based on the estimation of the error distribution in nonparametric regression models have been proposed in the recent literature. In the first part of the talk, we will revise the general idea of those testing procedures and present some examples (tests for the parametric form of the regression function, comparison of regression curves, tests about the equality of error distributions, and tests for the parametric form of the variance function). In the second part of the talk we will present some extensions and new perspectives of this kind of tests. Firstly, we will show how censored data can be incorporated to these models. Secondly, we will briefly present an estimator of the error distribution with multiple covariates, and show how it can be employed to test for additivity. Finally, we will discuss a test for a multiplicative structure in a dependent data setup. |