ABSTRACT Let be an independent and identically distributed (iid) sequence of interest random variables (rv) distributed as T. In censorship models, T is subject to random censoring by another rv C. Based on the so-called synthetic data, we define an M-estimator for the regression function of T given a functional covariate . Under standard assumptions on the kernel, bandwidth and small ball probabilities, we establish its strong consistency with rate and asymptotic normality. The asymptotic variance is given explicitly. Confidence bands are given and special cases are studied to show the generality of our work. Finally simulations are drawn to illustrate both quality of fit and robustness.

中文翻译：

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删失响应和功能回归量的稳健回归分析

摘要 让 是一个独立同分布（iid）的兴趣随机变量（rv）序列，分布为 T。在审查模型中，T 受到另一个 rv C 的随机审查。基于所谓的合成数据，我们定义了一个给定函数协变量 的 T 回归函数的 M 估计量。在核、带宽和小球概率的标准假设下，我们建立了它与速率和渐近正态性的强一致性。渐近方差是明确给出的。给出了置信区间并研究了特殊情况以显示我们工作的一般性。最后绘制模拟来说明拟合质量和鲁棒性。