Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0985.62039
Cheng, Shihong; Peng, Liang
Confidence intervals for the tail index. (English)
[J] Bernoulli 7, No.5, 751-760 (2001). ISSN 1350-7265

Summary: One of the best-known estimators for the tail index of a heavy-tailed distribution is the Hill estimator [{\it B.M. Hill}, Ann. Statist. 3, 1163-1174 (1975; Zbl 0323.62033)]. In this paper, confidence intervals based on the asymptotic normal approximation of Hill's estimator are studied. The coverage accuracy is evaluated and the theoretical optimal choice of the sample fraction for the one-sided confidence interval is given. One surprising finding is that the order of optimal coverage accuracy for the one-sided confidence interval depends on the sign of the second-order regular variation.

MSC 2000:: *62G32 Statistics of extreme values; tail inference
62G15 Nonparametric confidence regions, etc.
62F25 Parametric confidence regions, etc.
62F12 Asymptotic properties of parametric estimators

Keywords: tail index; Hill estimator; confidence intervals; coverage accuracy

Citations: Zbl 0323.62033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]