Abstract:
"The purpose of this dissertation is to establish asymptotic results of a kernel
type estimator of the regression function. This estimator is analogous
to the Nadaraya-Watson estimator but the response variable is subject to
twice censorship. We are conserned with the pointwise and uniform convergence
rate and asymptotic normality. The used convergence mode is
the almost complete convergence’s. This notion of almost complete convergence
leads to almost sure convergence.
We also develop the article of Messaci(2010) who introduced this estimator
and the one of Messaci and Nemouchi(2011) which proves a law of the
iterated logarithm of the estimator of Patilea et Rolin(2006) of the survival
function. Let us note that this estimator is explicitly involved in the expression
of the kernel estimator of the regression that is the subject of our
study. We will also give illustrations of our results on simulated data. Our
framework is that of nonparametric estimation of regression and censored
data"
