Open Access
September, 1991 On Tail Index Estimation Using Dependent Data
Tailen Hsing
Ann. Statist. 19(3): 1547-1569 (September, 1991). DOI: 10.1214/aos/1176348261


Let $X_1, X_2,\ldots$ be possibly dependent random variables having the same marginal distribution. Consider the situation where $\bar{F}(x) := P\lbrack X_1 > x\rbrack$ is regularly varying at $\infty$ with an unknown index $- \alpha < 0$ which is to be estimated. In the i.i.d. setting, it is well known that Hill's estimator is consistent for $\alpha^{-1}$, and is asymptotically normally distributed. It is the purpose of this paper to demonstrate that such properties of Hill's estimator extend considerably beyond the independent setting. In addition to some basic results derived under very general conditions, the case where the observations are strictly stationary and satisfy a certain mixing condition is considered in detail. Also a finite moving average sequence is studied to illustrate the results.


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Tailen Hsing. "On Tail Index Estimation Using Dependent Data." Ann. Statist. 19 (3) 1547 - 1569, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0738.62026
MathSciNet: MR1126337
Digital Object Identifier: 10.1214/aos/1176348261

Primary: 62F10
Secondary: 62G05

Keywords: order statistics , Parameter estimation , regular variation

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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