论文标题
非参数多输出中心向外的分位数回归
Nonparametric Multiple-Output Center-Outward Quantile Regression
论文作者
论文摘要
基于最近在Chernozhukov等人最近引入的多元中心外向分位数的新概念。 （2017）和Hallin等。 （2021），我们正在考虑非参数多出输出回归的问题。我们的方法定义了带有条件的条件分位数回归轮廓和区域，并具有给定的条件概率内容，而不论其基础分布如何；它们的图形构成嵌套的中心向外分位回归管。这些概念的经验对应物是构建的，产生了可解释的经验区域和轮廓，这些区域被证明在庞贝 - 霍斯多夫拓扑中始终如一地重建其种群版本。我们的方法完全不是参数，并且在包括异性恋和非线性趋势在内的模拟中表现良好。在一些实际数据集上说明了其作为数据分析工具的功率。
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.
