Censored and extreme losses: functional convergence and applications to tail goodness-of-fit
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| Format: | Preprint |
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2024
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| _version_ | 1866929466562838528 |
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| author | Bladt, Martin Øhlenschlæger, Christoffer |
| author_facet | Bladt, Martin Øhlenschlæger, Christoffer |
| contents | This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be used to obtain the distributions of pathwise functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_05862 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Censored and extreme losses: functional convergence and applications to tail goodness-of-fit Bladt, Martin Øhlenschlæger, Christoffer Methodology Statistics Theory This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be used to obtain the distributions of pathwise functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes. |
| title | Censored and extreme losses: functional convergence and applications to tail goodness-of-fit |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2408.05862 |