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

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 psi supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform consistency rate is established under alpha-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.

Automated summary

In this paper, a non-parametric M-estimator of the regression function is proposed and its asymptotic properties are investigated under the condition of random left truncation and right censoring of the response variable. Unlike most previous works, this estimator does not require the use of a bounded objective function, but can handle unbounded objective functions. The strong uniform consistency rate is established under alpha-mixing dependence.