Consider the extreme quantile region induced by the half-space depth function HD of the form Q={x∈R^d ∶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.
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机译：考虑由半空间深度函数HD诱导的极端分位数区域，其形式为Q = {x∈R^ d ∶HD（x，P）≤β}，使得对于给定的非常小的p> 0，PQ = p 。由于这涉及在数据云外部进行外推，因此很难通过完全非参数的过程来估计该区域。使用极值理论，我们构造了该分位数区域的自然半参数估计量，并证明了精确的一致性结果。仿真研究清楚地证明了我们的估算器的良好性能。通过将其应用于股票市场收益，我们使用了风险管理程序。
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