## The Annals of Applied Probability

### Weighted approximations of tail processes for $\beta$-mixing random variables

Holger Drees

#### Abstract

While the extreme value statistics for i.i.d data is well developed, much less is known about the asymptotic behavior of statistical procedures in the presence of dependence.We establish convergence of tail empirical processes to Gaussianlimits for $\beta$-mixing stationary time series. As a consequence, one obtains weighted approximations of the tail empirical quantile function that is based on a random sequence with marginal distribution belonging to the domain of attraction of an extreme value distribution. Moreover, the asymptotic normality is concluded for a large class of estimators of the extreme value index. These results are applied to stationary solutions of a general stochastic difference equation.

#### Article information

Source
Ann. Appl. Probab., Volume 10, Number 4 (2000), 1274-1301.

Dates
First available in Project Euclid: 22 April 2002

https://projecteuclid.org/euclid.aoap/1019487617

Digital Object Identifier
doi:10.1214/aoap/1019487617

Mathematical Reviews number (MathSciNet)
MR1810875

Zentralblatt MATH identifier
1073.60520

#### Citation

Drees, Holger. Weighted approximations of tail processes for $\beta$-mixing random variables. Ann. Appl. Probab. 10 (2000), no. 4, 1274--1301. doi:10.1214/aoap/1019487617. https://projecteuclid.org/euclid.aoap/1019487617

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