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首页> 外文期刊>Scandinavian journal of statistics >Linear censored quantile regression: A novel minimum-distance approach
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Linear censored quantile regression: A novel minimum-distance approach

机译：线性被审查量子回归：一种新的最小距离方法

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摘要

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.
机译：在本文中，我们调查了一种估计线性分位数回归的新程序，可能是可能的右缩短的响应。与主题的主要文献相反，我们提出了通过所谓的“检查”损失函数来规避条件量数的调整，这些损失函数源于Koenker和Bassett（1978）的影响力。相反，我们的建议通过最小化距离的替代度量来估计分量系数。事实上，我们的方法可以作为在给予协调因子的响应的条件分布的技术中的参数回归框架中的概括。这是通过宣传数据的主要文献已经依赖于某些非参数条件分布估计的动机。然后利用有效维度减少的思想，以便在这种情况下适应更高的维度设置。随后的广泛数值结果表明，这种方法基于检查功能为经典方法提供了强烈竞争的过程，实际上都是完整和审查的观察。从理论前景来看，在古典规则条件下获得了建议估算器的一致性和渐近常态。作为副产物，还获得了几个“双核”版条件Kaplan-Meier分配估计器的几个渐近结果，以及其相应的密度估计器，也可能对其自身感兴趣。然后，将我们的程序简要应用于准数据，然后用于进一步突出后者与缩短数据的定量回归估计的相关性。

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