Robust nonparametric equivariant M-estimators for the regression function have been extensively studied when the covariates are in Rk. In this paper, we derive strong uniform convergence rates for kernel-based robust equivariant M-regression estimator when the covariates are functional.

We consider robust testing on the regression parameter of a partially linear regression model, where missing responses are allowed. We derive the asymptotic behavior of the proposed test statistic under the null and contiguous alternatives. A numerical study is performed.