Consistent test for parametric models with right-censored data using projections

In the literature, there are several methods to test the adequacy of parametric models with right-censored data. However, these methods will lose effect when the predictors are medium-high dimensional. In this study, a projection-based test method is built, which acts as if the predictors were scalar even if they are multidimensional. The proposed test is shown to be consistent and can detect the alternative hypothesis converging to the null hypothesis at the rate n−r with 0≤r≤1∕2. Also, it is free from the choices of the subjective parameters such as bandwidth, kernel and weighting function. A wild bootstrap method is developed to determine the critical value of the test, which is shown to be robust to the model conditional heteroskedasticity. Simulation studies and real data analyses are conducted to validate the finite sample behavior of the proposed method.