On multivariate separating Hill estimator under estimated location and scatter

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On multivariate separating Hill estimator under estimated location and scatter. / Heikkilä, Matias; Dominicy, Yves; Ilmonen, Pauliina.

In: STATISTICS, 20.11.2018, p. 1-20.

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@article{5ba62a89fb6c48bdb0f6efd3bf4c53a2,
title = "On multivariate separating Hill estimator under estimated location and scatter",
abstract = "We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.",
keywords = "62G32, 62H12, elliptical distribution, extreme value index, Multivariate extreme value theory",
author = "Matias Heikkil{\"a} and Yves Dominicy and Pauliina Ilmonen",
year = "2018",
month = "11",
day = "20",
doi = "10.1080/02331888.2018.1548016",
language = "English",
pages = "1--20",
journal = "STATISTICS",
issn = "0233-1888",
publisher = "Taylor and Francis Ltd.",

}

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TY - JOUR

T1 - On multivariate separating Hill estimator under estimated location and scatter

AU - Heikkilä, Matias

AU - Dominicy, Yves

AU - Ilmonen, Pauliina

PY - 2018/11/20

Y1 - 2018/11/20

N2 - We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.

AB - We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.

KW - 62G32

KW - 62H12

KW - elliptical distribution

KW - extreme value index

KW - Multivariate extreme value theory

UR - http://www.scopus.com/inward/record.url?scp=85057343597&partnerID=8YFLogxK

U2 - 10.1080/02331888.2018.1548016

DO - 10.1080/02331888.2018.1548016

M3 - Article

SP - 1

EP - 20

JO - STATISTICS

JF - STATISTICS

SN - 0233-1888

ER -

ID: 30310889