TY - JOUR
T1 - A tail estimator for the index of the stable paretian distribution
AU - Mittnik, Stefan
AU - Paolella, Marc S.
AU - Rachev, Svetlozar T.
PY - 1998
Y1 - 1998
N2 - A new tail estimator for the index α of stable Paretian distributions is considered. The problem of specifying integer k, which determines the tail area used for estimation, is investigated for all three estimators, and shown that the optimal k value for the new estimator is highly insensitive to the true value of index α. As a result, in contrast to existing tail estimators such as the widely used Hill estimator, a simple rule for choosing k can be established. Finally, the small sample properties of the new estimator are examined.
AB - A new tail estimator for the index α of stable Paretian distributions is considered. The problem of specifying integer k, which determines the tail area used for estimation, is investigated for all three estimators, and shown that the optimal k value for the new estimator is highly insensitive to the true value of index α. As a result, in contrast to existing tail estimators such as the widely used Hill estimator, a simple rule for choosing k can be established. Finally, the small sample properties of the new estimator are examined.
KW - Hill estimator
KW - Pickands estimator
KW - Stable distributions
KW - Tail estimation
UR - http://www.scopus.com/inward/record.url?scp=0000322242&partnerID=8YFLogxK
U2 - 10.1080/03610929808832156
DO - 10.1080/03610929808832156
M3 - Article
AN - SCOPUS:0000322242
SN - 0361-0926
VL - 27
SP - 1239
EP - 1262
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 5
ER -