Electronic Journal of Statistics

Multivariate generalized linear-statistics of short range dependent data

Svenja Fischer, Roland Fried, and Martin Wendler

Full-text: Open access

Abstract

Generalized linear ($GL$-) statistics are defined as functionals of an $U$-quantile process and unify different classes of statistics such as $U$-statistics and $L$-statistics. We derive a central limit theorem for $GL$-statistics of strongly mixing sequences and arbitrary dimension of the underlying kernel. For this purpose we establish a limit theorem for $U$-statistics and an invariance principle for $U$-processes together with a convergence rate for the remaining term of the Bahadur representation.

An application is given by the generalized median estimator for the tail-parameter of the Pareto distribution, which is commonly used to model exceedances of high thresholds. We use subsampling to calculate confidence intervals and investigate its behaviour under independence and under strong mixing in simulations.

Article information

Source
Electron. J. Statist. Volume 10, Number 1 (2016), 646-682.

Dates
Received: December 2014
First available in Project Euclid: 7 March 2016

Permanent link to this document
http://projecteuclid.org/euclid.ejs/1457382317

Digital Object Identifier
doi:10.1214/16-EJS1124

Mathematical Reviews number (MathSciNet)
MR3471992

Zentralblatt MATH identifier
1332.62158

Subjects
Primary: 62G30: Order statistics; empirical distribution functions 60G10: Stationary processes
Secondary: 60F17: Functional limit theorems; invariance principles

Keywords
$GL$-statistics $U$-statistics strong mixing generalized median estimator tail parameter

Citation

Fischer, Svenja; Fried, Roland; Wendler, Martin. Multivariate generalized linear-statistics of short range dependent data. Electron. J. Statist. 10 (2016), no. 1, 646--682. doi:10.1214/16-EJS1124. http://projecteuclid.org/euclid.ejs/1457382317.


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