论文标题
加权平均分位数回归
Weighted-average quantile regression
论文作者
论文摘要
在本文中，我们介绍了加权平均分数回归框架，$ \ int_0^1 q_ {y | x}（u）ψ（u）ψ（u）du =x'β$，其中$ y $是一个因变量，$ x $是covariates的载体，$ q_ {y | x} $是$ y $ y $ y y y y y y y y y y y y y y y y y y $ x $ x $， $β$是参数的向量。我们认为，该框架在许多应用的设置中引起了人们的关注，并开发了参数向量$β$的估计器。我们表明，我们的估计器为$ \ sqrt t $ - 一致且渐近正常，平均零且易于估计的协方差矩阵，其中$ t $是可用样本的大小。我们通过在两个经验环境中应用估算器来证明我们的估计器的实用性。在第一个环境中，我们专注于财务数据并研究行业投资组合预期不足的因素结构。在第二个环境中，我们专注于工资数据，研究不平等和社会福利对常用个人特征的依赖。
In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)ψ(u)du = X'β$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $ψ$ is a weighting function, and $β$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $β$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.
