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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.

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