Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function
It is well known that a bivariate distribution belongs to the domain of attraction of an extreme value distribution G if and only if the marginals belong to the domain of attraction of the univariate marginal extreme value distributions and the dependence function converges to the stable tail dependence function of G. Hall and Welsh (1984,Ann. Statist.12, 1079-1084) and Drees (1997b,Ann. Statist., to appear) addressed the problem of finding optimal rates of convergence for estimators of the extreme value index of an univariate distribution. The present paper deals with the corresponding problem for the stable tail dependence function. First an upper bound on the rate of convergence for estimators of the stable tail dependence function is established. Then it is shown that this bound is sharp by proving that it is attained by the tail empirical dependence function. Finally, we determine the limit distribution of this estimator if the dependence function satisfies a certain second-order condition.
Volume (Year): 64 (1998)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description |
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- repec:ner:tilbur:urn:nbn:nl:ui:12-125712 is not listed on IDEAS
- Einmahl, J.H.J. & de Haan, L. & Xin, H., 1993.
"Estimating a multidimensional extreme-value distribution,"
Other publications TiSEM
2816eb0c-8f15-4111-94f5-6, School of Economics and Management.
- Einmahl, J. H. J. & Dehaan, L. & Huang, X., 1993. "Estimating a Multidimensional Extreme-Value Distribution," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 35-47, October.
- repec:ner:tilbur:urn:nbn:nl:ui:12-142070 is not listed on IDEAS
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:64:y:1998:i:1:p:25-47. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.