Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional probability content irrespective of the underlying distribution; their graphs constitute nested center-outward quantile regression tubes. Empirical counterparts of these concepts are constructed, yielding interpretable empirical regions and contours which are shown to consistently reconstruct their population versions in the Pompeiu-Hausdorff topology. Our method is entirely non-parametric and performs well in simulations including heteroskedasticity and nonlinear trends; its power as a data-analytic tool is illustrated on some real datasets.
翻译:根据最近在Chernozhukov等人(2017年)和Hallin等人(2021年)引入的多变量中向外微调新概念,我们正在考虑非参数多输出孔径回归的问题。我们的方法定义了嵌入的有条件中外向孔径回归轮廓和地区,其附带条件的概率含量不考虑基本分布;它们的图表构成嵌入中向外微量回归管。这些概念的实证对应方正在构建,产生可解释的经验区域和轮廓,显示它们能够一致地重建Pombeiu-Hausdorff 地形学的人口版本。我们的方法完全不是参数,在模拟中表现得非常好,包括三重力和非线性趋势;一些真实的数据集展示了它作为数据分析工具的力量。