Nonparametric lack-of-fit tests for parametric mean-regression models with censored data

We develop two kernel smoothing based tests of a parametric mean-regression model against a nonparametric alternative when the response variable is rightcensored. The new test statistics are inspired by the synthetic data and the weighted least squares approaches 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 tests are consistent against fixed alternatives, local Pitman alternatives and uniformly over alternatives in Hölder classes of functions of known regularity.