MODEL-FREE INFERENCE FOR TAIL RISK MEASURES
提出一种非参数框架，利用协变量中的辅助信息，对风险价值、预期亏损等尾部风险度量进行推断，构造两步广义经验似然检验统计量，无需方差估计，适用于序列相关数据。
Understanding uncertainty in estimating risk measures is important in modern financial risk management. In this paper we consider a nonparametric framework that incorporates auxiliary information available in covariates and propose a family of inferential methods for the value at risk, expected shortfall, and related risk measures. A two-step generalized empirical likelihood test statistic is constructed and is shown to be asymptotically pivotal without requiring variance estimation. We also show its validity when applied to a semiparametric index model. Asymptotic theories are established allowing for serially dependent data. Simulations and an empirical application to Canadian stock return index illustrate the finite sample behavior of the methodologies proposed.