This paper is devoted to the study of asymptotic properties of the kernel estimator of the robust regression function for stationary continuous-time and ergodic data. Such a dependence structure is an alternative to the strong mixing conditions usually assumed in functional time series analysis. More precisely, we consider the kernel type estimator of the robust regression function constructed from the stationary and continuous-time ergodic data $\text{◂(Xt,Yt)(Xt,Yt)▸}(X_t,Y_t)$ for $0\le t\le T$. Then, we establish the almost sure (with rate) pointwise convergence of this estimator. A simulation study was conducted in order to compare the performance of this method to the classical regression method.

中文翻译：

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平稳连续时间和遍历数据的 M 回归函数估计器的一致性结果

本文致力于研究平稳连续时间和遍历数据稳健回归函数核估计量的渐近性质。这种依赖结构是功能时间序列分析中通常假设的强混​​合条件的替代方案。更准确地说，我们考虑从平稳和连续时间遍历数据构造的稳健回归函数的核类型估计量$\text{◂(Xt,Yt)(Xt,Yt)▸}(X_{吨},{是}_{吨})$为了$0\le 吨\le 吨$. 然后，我们建立该估计量的几乎确定的（有速率的）逐点收敛。为了比较该方法与经典回归方法的性能，进行了模拟研究。