Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the first step, quantile regression is applied to each response separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional definition of quantiles, and can be used to capture important features of a multivariate response and assess the effects of covariates on the correlation structure. We apply the proposed method to analyze two different datasets.

中文翻译：

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具有多个结果的分位数回归残差的建模符号一致性

分位数回归允许描述标量响应变量的分位数如何依赖于一组预测变量。由于缺乏多元分位数的唯一定义，将分位数回归扩展到多元响应有些复杂。在本文中，我们描述了一种基于两步程序的简单方法：在第一步中，分位数回归分别应用于每个响应；第二步，通过多项式回归对残差符号的联合分布进行建模。所描述的方法不需要分位数的多维定义，可用于捕获多变量响应的重要特征并评估协变量对相关结构的影响。我们应用所提出的方法来分析两个不同的数据集。