@techreport{d6529c8a88654c03a064a63fd5097ffd,

title = "Estimation of Extreme Depth-Based Quantile Regions",

abstract = "Consider the extreme quantile region, induced by the halfspace depth function HD, of the form Q = fx 2 Rd : HD(x; P) g, such that PQ = p for a given, very small p > 0. This region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data. 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, halfspace depth, multivariate quantile, outlier detection, rare event, tail dependence",

author = "Y. He and J.H.J. Einmahl",

year = "2014",

month = may,

day = "29",

language = "English",

volume = "2014-035",

series = "CentER Discussion Paper",

publisher = "Econometrics",

type = "WorkingPaper",

institution = "Econometrics",

}