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arXiv 1912.02151econ.EMmath.STstat.MEstat.TH
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高维潜在面板分位数回归及其在资产定价中的应用

High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing

Alexandre Belloni, Mingli Chen, Oscar Hernan Madrid Padilla, Zixuan, Wang

摘要:

我们提出了一个线性面板分位数回归模型的推广,以适应\textit{sparse}和\textit{dense}部分:稀疏的意思,而可用的协变量的数量是大的,可能只有一个小得多的数量对每个条件分位数的响应变量有非零的影响,而密集的部分是由一个低秩矩阵,可以近似的潜在因素及其负载。这种结构对传统稀疏估计器(例如$\ell_1$惩罚分位数回归)和传统潜在因子估计器(例如PCA)造成问题。我们提出了一个新的估计过程,ADMM算法的基础上,由分位数损失函数与$\ell_1$ \textit{and}核范数正则化相结合。我们表明,在一般条件下,我们的估计可以一致估计的非零系数的协变量和潜在的低秩矩阵。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量应用于一个大维度的金融数据面板,并发现(i)一旦潜在因素得到控制,特征具有更稀疏的预测能力(ii)上分位数和下分位数的因子和系数与中位数不同。

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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