Estimation of Extreme Quantiles for Functions of Dependent Random Variables
Estimation of Extreme Quantiles for Functions of Dependent Random Variables
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因随机变量函数的极值分位数估计
DOI：
10.1111/rssb.12103
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发表时间：
2015
影响因子：
--
通讯作者：
Gong J
中科院分区：
文献类型：
--
作者：
Gong J
提出了一种估计多个相依随机变量函数极值分位数的新方法。与传统的方法相比，基于极值理论，我们不强加的条件下，尾部的基本分布承认一个近似的参数形式，而且，我们的估计利用了完整的观测数据。所提出的方法是半参数的，因为没有参数形式的边缘分布假设。但是我们利用最近在构造高维藤连接函数方面的发展，选择合适的二元连接函数来模拟联合依赖结构。因此，从拟合的联合分布中抽取的大自助样本产生的样本分位数被用作极值分位数的估计量。在分位数集与其截断集的贴近度以及截断集的经验逼近的正则性条件下，证明了该估计的相合性。仿真结果进一步证明了该方法的可靠性和鲁棒性。该方法进一步说明了一个真实的世界的例子在回测金融风险模型。
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast with the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The method proposed is semiparametric as no parametric forms are assumed on the marginal distributions. But we select appropriate bivariate copulas to model the joint dependence structure by taking advantage of the recent development in constructing large dimensional vine copulas. Consequently a sample quantile resulting from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile. This estimator is proved to be consistent under the regularity conditions on the closeness between a quantile set and its truncated set, and the empirical approximation for the truncated set. The simulation results lend further support to the reliable and robust performance of the method proposed. The method is further illustrated by a real world example in backtesting financial risk models.