英文标题：
《A Joint Quantile and Expected Shortfall Regression Framework》
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作者：
Timo Dimitriadis and Sebastian Bayer
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最新提交年份：
2017
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英文摘要：
We introduce a novel regression framework which simultaneously models the quantile and the Expected Shortfall (ES) of a response variable given a set of covariates. This regression is based on a strictly consistent loss function for the pair quantile and ES, which allows for M- and Z-estimation of the joint regression parameters. We show consistency and asymptotic normality for both estimators under weak regularity conditions. The underlying loss function depends on two specification functions, whose choice affects the properties of the resulting estimators. We find that the Z-estimator is numerically unstable and thus, we rely on M-estimation of the model parameters. Extensive simulations verify the asymptotic properties and analyze the small sample behavior of the M-estimator for different specification functions. This joint regression framework allows for various applications including estimating, forecasting, and backtesting ES, which is particularly relevant in light of the recent introduction of ES into the Basel Accords.
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中文摘要：
我们引入了一个新的回归框架，该框架同时对给定一组协变量的响应变量的分位数和预期短缺进行建模。该回归基于成对分位数和ES的严格一致损失函数，允许对联合回归参数进行M和Z估计。在弱正则条件下，我们证明了这两种估计量的相合性和渐近正态性。基本损失函数依赖于两个规格函数，其选择会影响结果估计量的性质。我们发现Z-估计在数值上是不稳定的，因此，我们依赖于模型参数的M-估计。大量的仿真验证了M估计的渐近性质，并分析了不同规格函数下M估计的小样本行为。该联合回归框架允许各种应用，包括估计、预测和回溯测试ES，鉴于最近将ES引入巴塞尔协议，这一点尤其相关。
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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：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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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