In this paper we study the M-estimation of the functional nonparametric regression when the response variable is subject to left-truncation by an other random variable. Under standard assumptions, we get the almost complete convergence rate of this robust estimate when the sample is an $$\alpha $$α-mixing sequence. This approach can be applied in time series analysis to the prediction problem. Our asymptotic results are confronted by some simulations study.

中文翻译：

---

随机左截断和函数时间序列模型下回归函数的 M 估计

在本文中，我们研究了当响应变量被其他随机变量左截断时，函数非参数回归的 M 估计。在标准假设下，当样本是 $$\alpha $$α-mixing 序列时，我们得到了这个稳健估计的几乎完全收敛率。这种方法可以应用于预测问题的时间序列分析。我们的渐近结果面临着一些模拟研究。