Robust regression analysis for a censored response and functional regressors

Let (Tn)n≥1 be an independent and identically distributed (iid) sequence of interest random variables (rv) distributed as T. In censorship models, T is subject to random censoring by another rv C. Based on the so-called synthetic data, we define an M-estimator for the regression function of T given a functional covariate χ. Under standard assumptions on the kernel, bandwidth and small ball probabilities, we establish its strong consistency with rate and asymptotic normality. The asymptotic variance is given explicitly. Confidence bands are given and special cases are studied to show the generality of our work. Finally simulations are drawn to illustrate both quality of fit and robustness.