DECONVOLVING KERNEL REGRESSION FUNCTION ESTIMATION BASED ON RIGHT CENSORED DATA
Abstract
In this study, we propose a new regression function estimator when the observa-
tion is contaminated in the convolution model with error in independent variable. We
want to examine the e ect of the error variables when the data is right censored. The
tail behavior of the characteristic function of the error distribution is used to describe
the optimum local and global rates of convergence of these kernel estimators. We show
that depending on the error is either ordinary smooth or super smooth, there are two
sorts of convergence rates in adjusted mean square error for the regression function
estimator. It is observed that the rate of convergence is slower in super smooth
model for both locally and globally, whereas it is faster in ordinary smooth model.
Furthermore, it is examined that in nonparametric regression function estimation, the
choice of the kernel K has very little impact on optimality (in the MSE sense), but
the bandwidth h has signi cant impact. Simulation are drawn for di erent sample
sizes in two di erent examples with 100 replications for each of the samples.