Estimation of extreme depth-based quantile regions

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2017 · Volume 79 · Issue 2

Abstract

Consider the extreme quantile region induced by the half-space depth function HD of the form, such thatfor a given, very smallp>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.

Keywords

Extreme value statistics, Half-space depth, Multivariate quantile, Outlier detection, Rare event, Tail dependence

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