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Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case
Author(s) -
KLÜPPELBERG CLAUDIA,
KUHN GABRIEL,
PENG LIANG
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00602.x
Subject(s) - tail dependence , mathematics , estimator , copula (linguistics) , parametric statistics , function (biology) , semiparametric model , parametric model , statistical physics , parametric equation , multivariate statistics , dimension (graph theory) , econometrics , statistics , combinatorics , physics , biology , geometry , evolutionary biology
Abstract. In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high‐dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non‐parametrically estimating a tail dependence function is very inefficient and fitting a parametric model to tail dependence functions is not robust. In this paper, we propose a semi‐parametric model for (asymptotically dependent) tail dependence functions via an elliptical copula. Under this model assumption, we propose a novel estimator for the tail dependence function, which proves favourable compared to the empirical tail dependence function estimator, both theoretically and empirically.