A new MOX Report entitled “Sign-Flip inference for spatial regression with differential regularization” by Cavazzutti, M.; Arnone, E.; Ferraccioli, F.; Galimberti, C.; Finos, L.; Sangalli, L.M. has appeared in the MOX Report Collection. Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/64-2024.pdf Abstract: We address the problem of performing inference on the linear and nonlinear terms of a semiparametric spatial regression model with differential regularization. For the linear term, we propose a new resampling procedure, based on (partial) sign-flipping of an appropriate transformation of the residuals of the model. The proposed resampling scheme can mitigate the bias effect, induced by the differential regularization. We prove that the proposed test is asymptotically exact. Moreover, we show by simulation studies that it enjoys very good control of Type-I error also in small sample scenarios, differently from parametric alternatives. Furthermore, we show that the proposed test has higher power with respect to recently proposed nonparametric tests on the linear term of semiparametric regression models with differential regularization. Concerning the nonlinear term, we develop three different inference approaches: a parametric test, and two nonparametric alternatives. The nonparametric tests are based on a sign-flip approach. One of these tests is proved to be asymptotically ! exact, wh ile the other is proved to be exact also for finite samples. Simulation studies highlight the very good control of Type-I error of the nonparametric approaches, while retaining high power.
