Quantile is an important measure in finance and quality assessment in service industry. In this paper, we model the temporal and cross-sectional interactive effect of the quantiles of large-dimensional time series by a latent quantile factor model. The factor loadings and scores are learnt with statistical guarantee via an iterative check-loss-minimization procedure. Without any moment constraint on the idiosyncratic errors, we correctly identify the common and idiosyncratic components for each variable. We obtained the statistical convergence rates of the minimization estimators. Bahardur representations for the estimated factor loadings and scores are provided under some mild conditions. Moreover, a robust method is proposed to select the number of factors consistently. Simulation experiments checked the validity of the theory. Our analysis on a financial data set shows the superiority of learning quantile factors in portfolio allocation over other state-of-the-art methods that learn mean factors.

翻译：分位数是金融和服务行业质量评估中的重要度量指标。本文通过潜在分位数因子模型刻画大维时间序列分位数的时间与截面交互效应。采用基于检查损失最小化的迭代方法，在统计保证下学习因子载荷与得分。无需对 idiosyncratic误差施加任何矩约束，即可正确识别各变量的共同成分与 idiosyncratic成分。我们获得了最小化估计量的统计收敛速率，并在温和条件下给出了估计因子载荷与得分的Bahardur表征。此外，提出了一种鲁棒方法以一致性地选择因子个数。模拟实验验证了理论的有效性。对金融数据集的分析表明，在投资组合配置中学习分位数因子优于其他学习均值因子的前沿方法。