The Annals of Statistics

Extremal Index Estimation for a Weakly Dependent Stationary Sequence

Tailen Hsing

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Abstract

Under stationarity and weak dependence, the statistical significance and the estimation of the extremal index are considered. It is shown that the distribution of the sample maximum can be uniformly approximated given the extremal index and the marginal distribution as the sample size increases. An adaptive procedure is proposed for estimating the extremal index. The procedure is shown to be asymptotically optimal in a class of estimators.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 2043-2071.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349409

Digital Object Identifier
doi:10.1214/aos/1176349409

Mathematical Reviews number (MathSciNet)
MR1245780

Zentralblatt MATH identifier
0797.62018

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators

Keywords
Adaptive estimation extremal index stationary sequence

Citation

Hsing, Tailen. Extremal Index Estimation for a Weakly Dependent Stationary Sequence. Ann. Statist. 21 (1993), no. 4, 2043--2071. doi:10.1214/aos/1176349409. https://projecteuclid.org/euclid.aos/1176349409


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