Nonparametric tests for semiparametric regression models

Abstract Semiparametric regression models have received considerable attention over the last decades, because of their flexibility and good finite sample performances. Here we propose an innovative nonparametric test for linear part models, based on random sign-flipping appropriate transformation residuals, that exploits a spectral decomposition residualizing matrix associated with model. The can be applied to vast class extensively used semiparametric roughness penalties, components defined one-dimensional, as well multi-dimensional domains, including, instance, univariate or multivariate splines. We prove asymptotic properties proposed test. Moreover, by means extensive simulation studies, show superiority respect current parametric alternatives, demonstrating its excellent control Type I error, accompanied power, even in challenging data scenarios, where instead alternatives fail.