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2016 Multivariate generalized linear-statistics of short range dependent data
Svenja Fischer, Roland Fried, Martin Wendler
Electron. J. Statist. 10(1): 646-682 (2016). DOI: 10.1214/16-EJS1124

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.

Citation

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Svenja Fischer. Roland Fried. Martin Wendler. "Multivariate generalized linear-statistics of short range dependent data." Electron. J. Statist. 10 (1) 646 - 682, 2016. https://doi.org/10.1214/16-EJS1124

Information

Received: 1 December 2014; Published: 2016
First available in Project Euclid: 7 March 2016

zbMATH: 1332.62158
MathSciNet: MR3471992
Digital Object Identifier: 10.1214/16-EJS1124

Subjects:
Primary: 60G10, 62G30
Secondary: 60F17

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 1 • 2016
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