分位数图形模型：预测与条件独立性 系统风险的应用

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摘要翻译：
我们提出了两种分位数图形模型--条件独立分位数图形模型（CIQGMs）和预测分位数图形模型（PQGMs）。CIQGMs通过计算每个分位数指标下的分布依赖结构来刻画分布的条件独立性。因此，CIQGMs可以用于验证因果图模型中的图结构(\cite{pearl2009causality,robins1986new,heckman2015causal}）。这些模型的一个主要优点是，我们可以将它们应用于由非高斯和不可分离的冲击驱动的大型变量集合。PQGMs通过非对称损失函数下的最佳线性预测子图来刻画统计相关性。PQGMs做出的假设比CIQGMs更弱，因为它们允许错误的规范。由于QGMS能够处理大量的变量集合并关注分布的特定部分，我们可以应用它们来量化尾部的相互依赖关系。由此产生的尾部风险网络可用于衡量系统性风险贡献，这有助于在理解下行市场运动下国际金融传染和收益依赖结构方面取得进展。我们发展了QGMs的估计和推理方法，重点是在高维情况下，其中图中的变量数相对于观测值数来说是大的。对于CIQGMs，这些方法和结果包括有效的罚函数同时选择，一致的收敛速度和同时有效的置信区域。我们还对PQGMs导出了类似的结果，其中包括在高维设置中处理错误规范、许多控制和连续的附加条件事件的惩罚分位数回归的新结果。
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英文标题：
《Quantile Graphical Models: Prediction and Conditional Independence with
  Applications to Systemic Risk》
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作者：
Alexandre Belloni, Mingli Chen and Victor Chernozhukov
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最新提交年份：
2019
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分类信息：

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：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。
--
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 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.
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PDF链接：
https://arxiv.org/pdf/1607.00286

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关键词：系统风险 分位数 独立性 independence distribution characterize 刻画 驱动 位数 CIQGMs