TY - JOUR
T1 - On kernel estimation of the second order rate parameter in multivariate extreme value statistics
AU - Goegebeur, Yuri
AU - Guillou, Armelle
AU - Qin, Jing
PY - 2017/9
Y1 - 2017/9
N2 - We introduce a flexible class of kernel type estimators of a second order parameter appearing in the multivariate extreme value framework. Such an estimator is crucial in order to construct asymptotically unbiased estimators of dependence measures, as e.g. the stable tail dependence function. We establish the asymptotic properties of this class of estimators under suitable assumptions. The behaviour of some examples of kernel estimators is illustrated by a simulation study in which they are also compared with a benchmark estimator of a second order parameter recently introduced in the literature.
AB - We introduce a flexible class of kernel type estimators of a second order parameter appearing in the multivariate extreme value framework. Such an estimator is crucial in order to construct asymptotically unbiased estimators of dependence measures, as e.g. the stable tail dependence function. We establish the asymptotic properties of this class of estimators under suitable assumptions. The behaviour of some examples of kernel estimators is illustrated by a simulation study in which they are also compared with a benchmark estimator of a second order parameter recently introduced in the literature.
KW - Multivariate extreme value statistics
KW - Second order parameter
KW - Stable tail dependence function
U2 - 10.1016/j.spl.2017.04.015
DO - 10.1016/j.spl.2017.04.015
M3 - Journal article
SN - 0167-7152
VL - 128
SP - 35
EP - 43
JO - Statistics & Probability Letters
JF - Statistics & Probability Letters
ER -