Unified Unconditional Regression for Multivariate Quantiles, M-Quantiles, and Expectiles
本文利用多维Huber函数，提出一种统一回归方法，用于建模多元因变量的无条件分位数、M分位数和期望分位数，并扩展了Firpo等人的工作，通过重新中心化影响函数的均值回归来评估协变量变化对响应变量无条件分布的影响。
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.