The main purpose of this paper is to estimate, semi-parametrically, the quantiles of a conditional distribution when the response is a real-valued random variable subject to a right-censorship phenomenon and the predictor takes values in an infinite dimensional space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a kernel-type estimator of the conditional quantile when the data are supposed to be selected from an underlying stationary and ergodic process. Then, under some general conditions, the uniform almost-complete convergence rate as well as the asymptotic distribution of the estimator are established. A numerical study, including simulated and real data application, is performed to illustrate the validity and the finite-sample performance of the considered estimator.

中文翻译：

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一般依赖结构下的单功能指数分位数回归

本文的主要目的是在响应是受右删失现象影响的实值随机变量并且预测变量取无限维空间中的值时，以半参数方式估计条件分布的分位数。我们假设解释变量和响应变量通过单索引结构相连。首先，当数据应该从底层的平稳和遍历过程中选择时，我们引入了条件分位数的核型估计器。然后，在一些一般条件下，建立了估计量的均匀几乎完全收敛速度和渐近分布。进行了包括模拟和实际数据应用在内的数值研究，以说明所考虑估计器的有效性和有限样本性能。