Estimation of extreme depth‐based quantile regions Series B Statistical methodology
针对由半空间深度函数定义的极端分位数区域，利用极值理论构建半参数估计量并证明其一致性，通过模拟和股票市场回报数据验证了其在风险管理中的有效性。
Consider the extreme quantile region induced by the half‐space depth function HD of the form Q={x∈Rd:HD(x,P)⩽β}, such that PQ=p for a given, very small p>0. Since this involves extrapolation outside the data cloud, this region can hardly be estimated through a fully non‐parametric procedure. Using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly demonstrates the good performance of our estimator. We use the procedure for risk management by applying it to stock market returns.