On Pickands coordinates in arbitrary dimensions
Pickands coordinates were introduced as a crucial tool for the investigation of bivariate extreme value models. We extend their definition to arbitrary dimensions and, thus, we can generalize many known results for bivariate extreme value and generalized Pareto models to higher dimensions and arbitrary extreme value margins. In particular we characterize multivariate generalized Pareto distributions (GPs) and spectral [delta]-neighborhoods of GPs in terms of best attainable rates of convergence of extremes, which are well-known results in the univariate case. A sufficient univariate condition for a multivariate distribution function (df) to belong to the domain of attraction of an extreme value df is derived. Bounds for the variational distance in peaks-over-threshold models are established, which are based on Pickands coordinates.
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): 92 (2005)
Issue (Month): 2 (February)
|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.:
- Falk, Michael & Reiss, Rolf-Dieter, 2003. "Efficient estimators and LAN in canonical bivariate POT models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 190-207, January.
- Deheuvels, Paul, 1991. "On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 429-439, November.
- Einmahl, John H.J. & de Haan, Laurens & Sinha, Ashoke Kumar, 1997.
"Estimating the spectral measure of an extreme value distribution,"
Stochastic Processes and their Applications,
Elsevier, vol. 70(2), pages 143-171, October.
- J Einmahl, .H. & de Haan, L. & Sinha, A., 1997. "Estimating the spectral measure of an extreme value distribution," Other publications TiSEM ac22e123-1e5d-448a-981e-a, Tilburg University, School of Economics and Management.
- 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.
- Jiménez, Javier Rojo & Villa-Diharce, Enrique & Flores, Miguel, 2001. "Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 159-191, February.
- Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
- Omey, E. & Rachev, S. T., 1991. "Rates of convergence in multivariate extreme value theory," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 36-50, July.
- de Haan, L. & Peng, L., 1997. "Rates of Convergence for Bivariate Extremes," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 195-230, May.
- de Oliveira, J. Tiago, 1989. "Intrinsic estimation of the dependence structure for bivariate extremes," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 213-218, August.
- Falk, Michael & Reiss, Rolf Dieter, 2002. "A characterization of the rate of convergence in bivariate extreme value models," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 341-351, October.
- Deheuvels, Paul & Tiago de Oliveira, José, 1989. "On the non-parametric estimation of the bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 315-323, September. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:426-453. 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.