Various indicators and measures of the real life procedures rise up as functionals of the quantile process of a parent random variable Z. However, Z can be observed only through a response in a linear model whose covariates are not under our control and the probability distribution of error terms is generally unknown. The problem is that of nonparametric estimation or other inference for such functionals. We propose an estimation procedure based on the averaged two-step regression quantile, recently developed by the authors, combined with an R-estimator of slopes of the linear model.

翻译：现实生活中的各种指标和度量往往源于母体随机变量Z的分位过程的泛函。然而，Z只能通过线性模型中的响应变量进行观测，且该模型的协变量不受我们控制，误差项的概率分布通常也未知。问题在于如何对这些泛函进行非参数估计或其他推断。我们提出一种基于作者近期提出的平均两步回归分位数的估计方法，并结合线性模型斜率的R估计量。