Significance tests are invaluable tools for detecting redundant covariates in regression, enabling the proposal of simpler, more parsimonious models. This is particularly relevant in nonparametric regression with high dimensional or functional data due to the effects of the curse of dimensionality on estimation and inference procedures. A new kernel-based test, designed to be robust against the curse of dimensionality, is presented in this contribution. This proposal is related to two of the most prominent approaches in the literature on significance tests: smoothing and empirical process-based tests. We provide a result establishing the asymptotic behavior of the proposed test statistic under independence and weak dependence assumptions.