Right-censored nonparametric regression with measurement error

This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley-James method (BJM), which is essentially based on the Kaplan-Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel deconvolution.The performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.