Extremal behaviour and convergence rates for sample--based geometric quantiles and half space depths
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911770545750016 |
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| author | Singha, Sibsankar Kratz, Marie Vadlamani, Sreekar |
| author_facet | Singha, Sibsankar Kratz, Marie Vadlamani, Sreekar |
| contents | We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and tail behaviour of the corresponding underlying distributions. The intricate interplay between the sample size and the parameter driving the extremal behaviour forms the main result of this analysis. In the process, we also fill certain gaps in the understanding of population versions of geometric quantile and halfspace depth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10789 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extremal behaviour and convergence rates for sample--based geometric quantiles and half space depths Singha, Sibsankar Kratz, Marie Vadlamani, Sreekar Statistics Theory We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and tail behaviour of the corresponding underlying distributions. The intricate interplay between the sample size and the parameter driving the extremal behaviour forms the main result of this analysis. In the process, we also fill certain gaps in the understanding of population versions of geometric quantile and halfspace depth. |
| title | Extremal behaviour and convergence rates for sample--based geometric quantiles and half space depths |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2306.10789 |