Synthetic data based nonparametric testing of parametric mean-regression models with censored data

We develop a kernel smoothing based test of a parametric mean-regression model against a nonparametric alternative when the response variable is rightcensored. The new test statistic is inspired by the synthetic data approach for estimating the parameters of a (non)linear regression model under censoring. The asymptotic critical values of our tests are given by the quantiles of the standard normal law. The test is consistent against any fixed alternative, against local Pitman alternatives and uniformly over alternatives in Holder classes of functions of known regularity.