Multivariate Hill Estimators

被引：12

作者：

Dominicy, Yves ^{[1
]}

Ilmonen, Pauliina ^{[2
]}

Veredas, David ^{[3
,4
]}

机构：

[1] Univ Libre Bruxelles, ECARES, Solvay Brussels Sch Econ & Management, Brussels, Belgium

[2] Aalto Univ, Sch Sci, Dept Math & Syst Anal, Espoo, Finland

[3] Vlerick Business Sch, Ghent, Belgium

[4] Univ Ghent, Ghent, Belgium

来源：

INTERNATIONAL STATISTICAL REVIEW | 2017年 / 85卷 / 01期

关键词：

Hill estimator; elliptical distribution; minimum covariance determinant; tail index; L-h norm; TAIL INDEX ESTIMATION; EXTREME-VALUE DISTRIBUTION; REGULAR VARIATION; DISTRIBUTIONS; DEPENDENCE; EXPONENT; QUANTILE; MAXIMUM; MODELS; LAW;

D O I：

10.1111/insr.12120

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We propose two classes of semi-parametric estimators for the tail index of a regular varying elliptical random vector. The first one is based on the distance between a tail probability contour and the observations outside this contour. We denote it as the class of separating estimators. The second one is based on the norm of an arbitrary order. We denote it as the class of angular estimators. We show the asymptotic properties and the finite sample performances of both classes. We also illustrate the separating estimators with an empirical application to 21 worldwide financial market indexes.

引用

页码：108 / 142

页数：35

共 57 条

[1]

[Anonymous], CREDIT RISK MEASUREM

[2] ON SOME LIMIT THEOREMS SIMILAR TO ARC-SIN LAW [J].

BREIMAN, L .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1965, 10 (02) :323-&

[3]

Caeiro F, 2008, REVSTAT-STAT J, V6, P1

[4] ESTIMATION OF EXTREME RISK REGIONS UNDER MULTIVARIATE REGULAR VARIATION [J].

Cai, Juan-Juan ;

Einmahl, John H. J. ;

De Haan, Laurens .

ANNALS OF STATISTICS, 2011, 39 (03) :1803-1826

[5] Central limit theorem and influence function for the MCD estimators at general multivariate distributions [J].

Cator, Eric A. ;

Lopuhaa, Hendrik P. .

BERNOULLI, 2012, 18 (02) :520-551

[6]

Christoffersen PF, 2012, ELEMENTS OF FINANCIAL RISK MANAGEMENT, 2ND EDITION, P1

[7] KERNEL ESTIMATES OF THE TAIL INDEX OF A DISTRIBUTION [J].

CSORGO, S ;

DEHEUVELS, P ;

MASON, D .

ANNALS OF STATISTICS, 1985, 13 (03) :1050-1077

[8] Using a bootstrap method to choose the sample fraction in tail index estimation [J].

Danielsson, J ;

de Haan, L ;

Peng, L ;

de Vries, CG .

JOURNAL OF MULTIVARIATE ANALYSIS, 2001, 76 (02) :226-248

[9] Comparison of tail index estimators [J].

de Haan, L ;

Peng, L .

STATISTICA NEERLANDICA, 1998, 52 (01) :60-70

[10]

de Haan L., 1998, Stochastic Models, V14, P849

← 1 2 3 4 5 6 →