Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

Abstract

In this paper, we propose a non parametric M-estimator of the regression function and we investigate its asymptotic properties, when the response variable is subject to both random left truncation and right censoring. In most works, non parametric M-estimation requires the use of an objective function ψ supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform consistency rate is established under α-mixing dependence. A large simulation study with one and bi-dimensional regressor is conducted for fixed and local bandwidths to highlight the good behavior of our estimator