Deconvolving Kernel Regression Function Estimation Based On Right Censored Data

Music City Center 

In this study, we propose a novel regression function estimator for scenarios involving errors-in-variables within a convolution model, particularly when the data are subject to right-censoring. By leveraging the tail behavior of the characteristic function of the error distribution, we establish the optimal local and global convergence rates for the kernel estimators. Our results reveal thatthe convergence rate depends on the smoothness of the error distribution: It is slower for super smooth errors and faster for ordinary smooth errors, both locally and globally. Importantly, we demonstrate that while the choice of kernel K has a negligible impact on the optimality of the mean square error (MSE), the bandwidth h plays a critical role. Through simulations across varying sample sizes and 100 replications per setting, we validate the theoretical findings. Finally, we apply the proposed estimator to analyze the relationship between advanced lung cancer cases and Karnofsky Performance Scores, offering practical insight into this medical context.

Kernel Regression

Deconvolution

Right Censored Data

Additive Measurement Errors 

Section on Nonparametric Statistics