TY - JOUR
T1 - Estimating the spectral measure of an extreme value distribution
AU - Einmahl, J.H.J.
AU - Haan, de, L.
AU - Sinha, A.K.
PY - 1997
Y1 - 1997
N2 - Let (X1, Y1), (X2, Y2),…, (Xn, Yn) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.
AB - Let (X1, Y1), (X2, Y2),…, (Xn, Yn) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.
U2 - 10.1016/S0304-4149(97)00065-3
DO - 10.1016/S0304-4149(97)00065-3
M3 - Article
SN - 0304-4149
VL - 70
SP - 143
EP - 171
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -