Efficient estimators and LAN in canonical bivariate POT models
Bivariate generalized Pareto distributions (GPs) with uniform margins are introduced and elementary properties such as peaks-over-threshold (POT) stability are discussed. A unified parameterization with parameter [theta][set membership, variant][0,1] of the GPs is provided by their canonical parameterization. We derive efficient estimators of [theta] and of the dependence function of the GP in various models and establish local asymptotic normality (LAN) of the loglikelihood function of a 2x2 table sorting of the observations. From this result we can deduce that the estimator of [theta] suggested by Falk and Reiss (2001, Statist. Probab. Lett. 52, 233-242) is not efficient, whereas a modification actually is.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 84 (2003)
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|
References listed on IDEAS
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.:
- Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
- Falk, Michael & Reiss, Rolf-Dieter, 2001. "Estimation of canonical dependence parameters in a class of bivariate peaks-over-threshold models," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 233-242, April.
- Lu, Jye-Chyi & Bhattacharyya, Gouri K., 1991. "Inference procedures for bivariate exponential model of Gumbel," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 37-50, July.
- E. Kaufmann & R. Reiss, 1993. "Strong convergence of multivariate point processes of exceedances," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 433-444, September.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:84:y:2003:i:1:p:190-207. 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: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.