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摘要翻译：
我们提出了线性面板分位数回归模型的一个推广，以同时适应\textit{稀疏}和\textit{稠密}两个部分：稀疏是指当可用的协变量数目很大时，可能只有少得多的协变量对响应变量的每个条件分位数有非零的影响；而稠密部分则用一个低秩矩阵来表示，该矩阵可以用潜在因素及其载荷来近似。这种结构给传统的稀疏估计（如$\ell_1$-惩罚分位数回归）和传统的潜在因子估计（如PCA）带来了问题。在ADMM算法的基础上，提出了一种将分位数损失函数与核范数正则化和核范数正则化相结合的估计方法。在一般条件下，我们证明了我们的估计可以一致地估计协变量的非零系数和潜在的低秩矩阵。我们提出的模型具有“特征+潜在因素”的资产定价模型解释：我们将我们的模型和估计器应用于一个大维金融数据面板，发现(i)当潜在因素被控制时，特征具有更少的预测能力(ii)上分位数和下分位数的因素和系数与中位数不同。
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英文标题：
《High Dimensional Latent Panel Quantile Regression with an Application to
Asset Pricing》
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作者：
Alexandre Belloni, Mingli Chen, Oscar Hernan Madrid Padilla, Zixuan
(Kevin) Wang
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最新提交年份：
2019
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分类信息：
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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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We propose a generalization of the linear panel quantile regression model to accommodate both \textit{sparse} and \textit{dense} parts: sparse means while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional sparse estimators, such as the $\ell_1$-penalised Quantile Regression, and for traditional latent factor estimator, such as PCA. We propose a new estimation procedure, based on the ADMM algorithm, consists of combining the quantile loss function with $\ell_1$ \textit{and} nuclear norm regularization. We show, under general conditions, that our estimator can consistently estimate both the nonzero coefficients of the covariates and the latent low-rank matrix. Our proposed model has a "Characteristics + Latent Factors" Asset Pricing Model interpretation: we apply our model and estimator with a large-dimensional panel of financial data and find that (i) characteristics have sparser predictive power once latent factors were controlled (ii) the factors and coefficients at upper and lower quantiles are different from the median.
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PDF链接：
https://arxiv.org/pdf/1912.02151
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