Abstract
Summary 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.
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More From: Journal of the Royal Statistical Society Series B: Statistical Methodology
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