Statistical inference for nonparametric censored regression

Nonparametric regression is of primary importance in many statistical applications. For the data with censored outcomes, how to construct a confidence band for a regression function is a basic issue but has limited research. We propose a procedure to construct the pointwise and simultaneous confidence bands for a regression function based on a debiased estimator, which is proposed by correcting the bias of the original kernel regression estimator. The corresponding theoretical properties such as consistency, convergence rates, and the asymptotic distribution of the proposed estimator are also derived. Furthermore, we carry out extensive simulation studies and a real data example from the German Breast Cancer study to evaluate the finite sample performance of the proposed method.