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摘要翻译：
在普通分位数回归中，每次估计不同阶数的分位数。另一种方法，称为分位数回归系数建模(QRCM)，是将分位数回归系数建模为分位数阶的参数函数。本文描述了QRCM范式如何应用于纵向数据。我们引入了一个两级分位数函数，其中两个不同的分位数回归模型用来描述被试内反应和个体效应的（条件）分布。我们提出了一种新的惩罚固定效应估计，并讨论了它相对于基于$ell_1$和$ell_2$惩罚的标准方法的优点。我们给出了模型的可辨识性条件，导出了模型的渐近性质，描述了拟合优度度量和模型选择准则，给出了仿真结果，并讨论了一个应用。该方法已在R包QRCM中实现。
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英文标题：
《Parametric Modeling of Quantile Regression Coefficient Functions with
Longitudinal Data》
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作者：
Paolo Frumento, Matteo Bottai and Iv\'an Fern\'andez-Val
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最新提交年份：
2020
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/2006.00160
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