A kernel-based framework for covariate significance tests in nonparametric regression

It is well known that nonparametric regression estimation and inference procedures are subject to the curse of dimensionality. Moreover, model interpretability usually decreases with the data dimension. Therefore, model-free variable selection procedures and, in particular, covariate significance tests, are invaluable tools for regression modelling as they help to remove irrelevant covariates. In this contribution, we provide a general framework, based on recent developments in the theory of kernel-based characterizations of null conditional expectations, for testing the significance of a subgroup of Hilbert space-valued covariates in a nonparametric regression model. Moreover, we propose a test designed to be robust against the curse of dimensionality and we provide some asymptotic results regarding the distribution of the test statistic under the null hypothesis of non-significant covariates as well as under fixed and local alternatives. Regarding the test calibration, we present and prove the consistency of a multiplier bootstrap scheme. An extensive simulation study is conducted to assess the finite sample performance of the test. We also apply our test in a real data scenario