Abstract
The authors recently proved in Martig and Hüsler (2016) that the likelihood moment estimators are consistent estimators for the parameters of the Generalized Pareto distribution for the case where the underlying data arises from a (stationary) linear process with heavy-tailed innovations. In this paper we derive the bivariate asymptotic normality under some additional assumptions and give an explicit example on how to check these conditions by using asymptotic expansions. Some finite sample comparisons are presented to investigate the bias and variance behavior for some of the estimators.
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Acknowledgments
The authors want to thank William P. McCormick for his contributions and very thorough explanations regarding the asymptotic tail expansions. Another special thanks go to the reviewers, the associate editor and the editor-in-chief for their attentive corrections and their valuable inputs.
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Martig, L., Hüsler, J. Asymptotic normality of the likelihood moment estimators for a stationary linear process with heavy-tailed innovations. Extremes 21, 1–26 (2018). https://doi.org/10.1007/s10687-017-0301-9
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DOI: https://doi.org/10.1007/s10687-017-0301-9
Keywords
- Generalized Pareto distribution
- Linear processes
- Heavy-tailed data
- Likelihood moment estimators
- Asymptotic normality