Estimation of the Pareto and related distributions - A reference-intrinsic approach

We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capita...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2023-02, Vol.52 (3), p.523-542
Main Authors: Sharpe, James, Juárez, Miguel A.
Format: Article
Language:English
Subjects:
Generalized Pareto distribution
intrinsic loss
invariance
reference prior
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Summary:We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalized Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2021.1916826