In this paper, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber's function. To assess the impact of changes in the covariates across the entire unconditional distribution of the responses, we extend the work of Firpo et al. (2009) by running a mean regression of the recentered influence function on the explanatory variables. We discuss the estimation procedure and establish the asymptotic properties of the derived estimators. A data-driven procedure is also presented to select the tuning constant of the Huber's function. The validity of the proposed methodology is explored with simulation studies and through an application using the Survey of Household Income and Wealth 2016 conducted by the Bank of Italy.

翻译：本文基于多维Huber函数，开发了一种统一的回归方法来对多元因变量的无条件分位数、M-分位数及期望分位数进行建模。为评估协变量变化对响应变量整个无条件分布的影响，我们通过对解释变量进行重新中心化影响函数的均值回归，扩展了Firpo等人(2009)的研究工作。我们讨论了估计过程，并建立了所得估计量的渐近性质。此外，还提出了一种数据驱动的方法来选择Huber函数的调谐常数。通过模拟研究以及基于意大利银行2016年家庭收入与财富调查的应用分析，验证了所提方法的有效性。