Strong Convergence of Peaks Over a Threshold
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917659695644672 |
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| author | Padoan, Simone A. Rizzelli, Stefano |
| author_facet | Padoan, Simone A. Rizzelli, Stefano |
| contents | Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto distribution} $H_γ(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold $t$, where $s(t)$ is a suitable norming function. In this paper we study the rate of convergence of $F_t(s(t)\cdot)$ to $H_γ$ in variational and Hellinger distances and translate it into that regarding the Kullback-Leibler divergence between the respective densities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02171 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong Convergence of Peaks Over a Threshold Padoan, Simone A. Rizzelli, Stefano Probability Statistics Theory 60G70, 62F12, 62G20 Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto distribution} $H_γ(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold $t$, where $s(t)$ is a suitable norming function. In this paper we study the rate of convergence of $F_t(s(t)\cdot)$ to $H_γ$ in variational and Hellinger distances and translate it into that regarding the Kullback-Leibler divergence between the respective densities. |
| title | Strong Convergence of Peaks Over a Threshold |
| topic | Probability Statistics Theory 60G70, 62F12, 62G20 |
| url | https://arxiv.org/abs/2301.02171 |