论文标题
具有纵向数据的分位数回归系数函数的参数建模
Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data
论文作者
论文摘要
在普通的分位数回归中，一次估计一个不同顺序的分位数。一种替代方法称为分位数回归系数建模（QRCM），是将分位数回归系数模拟为分位数阶的参数函数。在本文中，我们描述了如何将QRCM范式应用于纵向数据。我们引入了两级分位数函数，其中使用了两个不同的分位回归模型来描述受试者内响应的（条件）分布和个体效应的分布。我们提出了一种新型的惩罚固定效果估计器，并讨论了基于$ \ ell_1 $和$ \ ell_2 $惩罚的标准方法的优势。我们提供模型可识别性条件，得出渐近性能，描述拟合优度和模型选择标准，呈现模拟结果并讨论应用程序。提出的方法已在R软件包QRCM中实现。
In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the QRCM paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on $\ell_1$ and $\ell_2$ penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.
