Extremal quantile regression
Extremal quantile regression
复制标题
DOI：
10.1214/009053604000001165
复制
发表时间：
2005-04-01
影响因子：
4.5
通讯作者：
Chernozhukov, V
中科院分区：
文献类型：
--
作者：
Chernozhukov, V
分位数回归是估计给定协变量向量X的响应Y的条件分位数的重要工具。它不仅可以用于测量分布中心的协变量的影响。而且在上尾和下尾中也是如此。本文发展了尾部分位数回归理论。具体地说，研究了尾部限制在最小吸引域且在回归变量值的尾部等价下闭的线性分位数回归模型的极值（极值阶和中间阶）分位数回归估计的大样本性质.这种建模设置结合了极值理论的限制与领先的同方差和异方差线性规范的回归分析。在大样本下，极阶回归分位数弱收敛于依赖于回归变量的Poisson过程随机积分的argmin泛函，而中间回归分位数及其泛函收敛于方差矩阵依赖于尾参数和回归变量设计的法向量.
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution. but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically, it obtains the large sample properties of extremal (extreme order and intermediate order) quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values. This modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis. In large samples, extreme order regression quantiles converge weakly to argmin functionals of stochastic integrals of Poisson processes that depend on regressors, while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design.