In this article, we investigate a new procedure for the estimation of a linear quantile regression with possibly right‐censored responses. Contrary to the main literature on the subject, we propose in this context to circumvent the formulation of conditional quantiles through the so‐called “check” loss function that stems from the influential work of Koenker and Bassett (1978). Instead, our suggestion is here to estimate the quantile coefficients by minimizing an alternative measure of distance. In fact, our approach could be qualified as a generalization in a parametric regression framework of the technique consisting in inverting the conditional distribution of the response given the covariates. This is motivated by the knowledge that the main literature for censored data already relies on some nonparametric conditional distribution estimation as well. The ideas of effective dimension reduction are then exploited in order to accommodate for higher dimensional settings as well in this context. Extensive numerical results then suggest that such an approach provides a strongly competitive procedure to the classical approaches based on the check function, in fact both for complete and censored observations. From a theoretical prospect, both consistency and asymptotic normality of the proposed estimator for linear regression are obtained under classical regularity conditions. As a by‐product, several asymptotic results on some “double‐kernel” version of the conditional Kaplan–Meier distribution estimator based on effective dimension reduction, and its corresponding density estimator, are also obtained and may be of interest on their own. A brief application of our procedure to quasar data then serves to further highlight the relevance of the latter for quantile regression estimation with censored data.

中文翻译：

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线性删失分位数回归：一种新颖的最小距离方法

在本文中，我们研究了一种估计线性分位数回归的新方法，可能带有右删失的响应。与该主题的主要文献相反，我们建议在这种情况下通过Koenker和Bassett（1978）的有影响的工作，通过所谓的“检查”损失函数来规避条件分位数的制定。相反，我们的建议是通过最小化距离的替代度量来估算分位数系数。实际上，我们的方法可以被认为是该技术的参数回归框架中的一般化，其归纳在于将给定协变量的响应的条件分布求逆。这是由以下知识所激发的，即用于审查数据的主要文献也已经依赖于某些非参数条件分布估计。然后利用有效尺寸减小的思想以便在这种情况下也适应更高的尺寸设置。然后，大量的数值结果表明，这种方法为基于检查功能的经典方法提供了一个强有力的竞争程序，实际上无论是对于完整的还是经审查的观测结果而言。从理论上看，在经典正则条件下，可以得到线性估计的估计量的一致性和渐近正态性。作为副产品，基于有效维数缩减的条件Kaplan-Meier分布估计量的某些“双核”版本上的一些渐近结果，还获得了它及其相应的密度估计器，它们可能自己感兴趣。然后，将我们的程序简短地应用于类星体数据，可以进一步突出后者与带删失数据的分位数回归估计的相关性。