TY  - JOUR
ID  - Helal2016
LB  - Helal2016
AU  - Helal, Nacéra
AU  - Saïd, Elias Ould
TI  - Kernel conditional quantile estimator under left truncation for functional regressors
ST  - Kernel conditional quantile estimator under left truncation for functional regressors
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 1
SP  - 25
EP  - 48
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.1.25
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.1.25
AB  - Let \(Y\) be a random real response which is subject to left-truncation by another random variable \(T\). In this paper, we study the kernel conditional quantile estimation when the covariable \(X\) takes values in an infinite-dimensional space. A kernel conditional quantile estimator is given under some regularity conditions, among which in the small-ball probability, its strong uniform almost sure convergence rate is established. Some special cases have been studied to show how our work extends some results given in the literature. Simulations are drawn to lend further support to our theoretical results and assess the behavior of the estimator for finite samples with different rates of truncation and sizes.
KW  - almost sure convergence
KW  - functional variables
KW  - kernel estimator
KW  - Lynden-Bell estimator
KW  - small-ball probability
KW  - truncated data
SN  - 1232-9274
ER  -