Nonparametric Lack-of-fit Tests for Parametric Mean-Regression Model with Censored Data

We develop two kernel smoothing based tests of a parametric mean-regressionmodel against a nonparametric alternative when the response variable is right-censored. The new test statistics are inspired by the synthetic data and the weightedleast squares approaches for estimating the parameters of a (non)linear regressionmodel under censoring. The asymptotic critical values of our tests are given by thequantiles of the standard normal law. The tests are consistent against ¯xed alter-natives, local Pitman alternatives and uniformly over alternatives in HÄolder classesof functions of known regularity.