In this paper, we establish weak consistency and asymptotic normality of an M-estimator of the regression function for left truncated and right censored (LTRC) model, where it is assumed that the observations form a stationary alpha-mixing sequence. The result holds with unbounded objective function, and are applied to derive weak consistency and asymptotic normality of a kernel classical regression curve estimate. We also obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and censored distribution under dependence, which are useful results for our study and other LTRC strong mixing framework. Some simulations are drawn to illustrate the results for finite sample.

翻译：本文针对左截尾右删失（LTRC）模型，建立了回归函数M估计量的弱相合性与渐近正态性，其中假设观测值构成平稳α-混合序列。该结论在无界目标函数下成立，并应用于推导核经典回归曲线估计的弱相合性与渐近正态性。此外，在相依性条件下，我们获得了寿命分布与删失分布乘积限估计量的均匀弱收敛速度，这一结果对本研究及其他LTRC强混合框架具有重要价值。最后通过模拟实验验证了有限样本下的结论。