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.

中文翻译：

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α混合条件下不完全数据的回归函数M估计的强一致一致性率

在本文中，我们提出了回归函数的非参数M估计，并研究了当响应变量同时受到随机左截断和右删失的影响时其渐近性质。在大多数工作中，非参数M估计需要使用假定为有界的目标函数ψ。结果在这里具有无限目标函数。在α-混合依赖性下建立了很强的均匀一致性率。针对固定带宽和局部带宽进行了带有一维和二维回归的大型仿真研究，以突出我们的估算器的良好行为。