标题： 分位数图模型：预测与条件独立性及其在系统性风险中的应用 显示英文标题

标题： Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk

摘要： 我们提出了两种类型的分位数图模型（QGMs）——条件独立分位数图模型（CIQGMs）和预测分位数图模型（PQGMs）。 CIQGMs 通过在每个分位数指数处评估分布的依赖结构来表征分布的条件独立性。因此，CIQGMs 可用于验证因果图模型（\cite{pearl2009causality, robins1986new, heckman2015causal}）中的图结构。这些模型的一个主要优势在于可以应用于由非高斯和非可分离冲击驱动的大规模变量集合。 PQGMs 则通过在不对称损失函数下的最佳线性预测器的图来表征统计依赖关系。与 CIQGMs 相比，PQGMs 假设更弱，因为它们允许模型误设。由于 QGMs 能够处理大规模变量集合并关注分布的特定部分，我们可以将其应用于量化尾部相依性。由此产生的尾部风险网络可用于衡量系统性风险贡献，有助于理解国际金融传染以及下行市场运动下的回报依赖结构。 我们针对 QGMs 开发了估计和推断方法，重点是高维情况，即图中的变量数量远大于观测值的数量。对于 CIQGMs，这些方法和结果包括有效的同时选择惩罚函数、一致的收敛速率以及同时有效的置信区域。我们还为 PQGMs 推导出类似的结果，其中包括高维设置下处理误设、许多控制变量以及连续附加条件事件的惩罚分位数回归的新结果。 显示英文摘要

摘要： We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by evaluating the distributional dependence structure at each quantile index. As such, CIQGMs can be used for validation of the graph structure in the causal graphical models (\cite{pearl2009causality, robins1986new, heckman2015causal}). One main advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. PQGMs characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. Because of QGMs' ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements. We develop estimation and inference methods for QGMs focusing on the high-dimensional case, where the number of variables in the graph is large compared to the number of observations. For CIQGMs, these methods and results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.