Moment Estimator-Based Extreme Quantile Estimation with Erroneous Observations: Application to Elliptical Extreme Quantile Region Estimation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929712055451648 |
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| author | Pere, Jaakko Ilmonen, Pauliina Viitasaari, Lauri |
| author_facet | Pere, Jaakko Ilmonen, Pauliina Viitasaari, Lauri |
| contents | In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and in corresponding extreme quantile estimation. We consider all, short-, light-, and heavy-tailed distributions. In particular, we derive conditions under which the error is asymptotically negligible. As an application, we consider affine equivariant extreme quantile region estimation under multivariate elliptical distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moment Estimator-Based Extreme Quantile Estimation with Erroneous Observations: Application to Elliptical Extreme Quantile Region Estimation Pere, Jaakko Ilmonen, Pauliina Viitasaari, Lauri Statistics Theory 62G32 (Primary) 62H12 (Secondary) In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and in corresponding extreme quantile estimation. We consider all, short-, light-, and heavy-tailed distributions. In particular, we derive conditions under which the error is asymptotically negligible. As an application, we consider affine equivariant extreme quantile region estimation under multivariate elliptical distributions. |
| title | Moment Estimator-Based Extreme Quantile Estimation with Erroneous Observations: Application to Elliptical Extreme Quantile Region Estimation |
| topic | Statistics Theory 62G32 (Primary) 62H12 (Secondary) |
| url | https://arxiv.org/abs/2502.08510 |