Model checking for partial linear model with right censored response

In this paper, we aim to check whether the nonparametric part in a partial linear regression model is parametric or not in the presence of right censored response. We propose a test statistics which can be considered as a kernel based smoothing estimator of some moment condition. We investigate our proposed test' asymptotic properties under the null and local alternative hypothesis. Simulation studies are carried out to illustrate the performance of the sizes and powers of our test. We also apply our methodology to a study on multiple myeloma.