Selecting the optimal sample fraction in univariate extreme value estimation
In general, estimators of the extreme value index of i.i.d. random variables crucially depend on the sample fraction that is used for estimation. In case of the well-known Hill estimator the optimal number knopt of largest order statistics was given by Hall and Welsh (1985) as a function of some parameters of the unknown distribution function F, which was assumed to admit a certain expansion. Moreover, an estimator of knopt was proposed that is consistent if a second-order parameter [rho] of F belongs to a bounded interval. In contrast, we introduce a sequential procedure that yields a consistent estimator of knopt in the full model without requiring prior information about [rho]. Then it is demonstrated that even in a more general setup the resulting adaptive Hill estimator is asymptotically as efficient as the Hill estimator based on the optimal number of order statistics. Finally, it is shown by Monte Carlo simulations that also for moderate sample sizes the procedure shows a reasonable performance, which can be improved further if [rho] is restricted to bounded intervals.
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): 75 (1998)
Issue (Month): 2 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://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.:
- Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
- Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:75:y:1998:i:2:p:149-172. 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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.