Comparative study on excess distribution estimation in iid settings

Taku Moriyama

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 7, 2092-2108

Abstract: This study considers excess distribution estimation in iid settings. There are two ways for the estimation; the fitting to the generalized Pareto distribution and the fully non parametric estimation. The fitting estimator is justified by the approximation proven in the extreme value theory; however, the accuracy depends on how extremely large the target is. The non parametric estimator does not need an approximation and has the advantage of wide applicability. This study conducts both theoretical and numerical comparative study on excess distribution estimation. Asymptotic convergence rates of two estimators are obtained, and the mean integrated squared errors are numerically surveyed by simulation study. An illustrative example of Abisko rainfall amount is presented.

Date: 2025
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DOI: 10.1080/03610926.2024.2358864

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