We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.

中文翻译：

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经验回归分位数过程

当测量或受控实体依赖于不受我们控制的外生变量时，我们解决了估计基于分位数的统计泛函的问题。作为合适的工具，我们提出了平均回归分位数的经验过程。它部分掩盖了协变量的影响，并具有其他便于应用的特性，例如在具有协变量的情况下进行各种类型的连贯风险度量。