EXTREME CONDITIONAL EXPECTILE ESTIMATION IN HEAVY-TAILED HETEROSCEDASTIC REGRESSION MODELS
EXTREME CONDITIONAL EXPECTILE ESTIMATION IN HEAVY-TAILED HETEROSCEDASTIC REGRESSION MODELS
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DOI：
10.1214/21-aos2087
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发表时间：
2021-12-01
影响因子：
4.5
通讯作者：
Usseglio-Carleve, Antoine
中科院分区：
文献类型：
--
作者：
Girard, Stephane;Stupfler, Gilles;Usseglio-Carleve, Antoine
弹片定义了分位数的最小二乘类比。在过去十年中，它们一直是精算和金融风险评估领域大量研究的焦点。在最近的一系列论文中，研究了使用独立和同分布重尾观测的无条件极端期望子的行为和估计。本文建立了重尾噪声异方差回归模型极值条件期望估计的一般理论；我们的方法得到了对重尾回归模型中基于残差的极值估计量的独立兴趣的一般结果的支持，并且旨在处理具有大但固定维度的协变量。我们展示了如何将我们的结果应用于广泛的重要示例，其中包括线性模型，单指标模型以及ARMA和GARCH时间序列模型。我们的估算器在数值模拟研究和真实的精算和财务数据集上展示。
Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with covariates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which are linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.