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Estimation of extreme depth‐based quantile regions
Author(s) -
He Yi,
Einmahl John H. J.
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12163
Subject(s) - quantile , extreme value theory , estimator , extrapolation , econometrics , consistency (knowledge bases) , mathematics , stock (firearms) , statistics , geography , geometry , archaeology
Summary 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 P Q = 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.