Asymptotic behavior of clusters in hierarchical species sampling models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917894006243328 |
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| author | Favaro, Stefano Feng, Shui Paguyo, J. E. |
| author_facet | Favaro, Stefano Feng, Shui Paguyo, J. E. |
| contents | Consider a sample of size $N$ from a population governed by a hierarchical species sampling model. We study the large $N$ asymptotic behavior of the number ${\bf K}_N$ of clusters and the number ${\bf M}_{r,N}$ of clusters with frequency $r$ in the sample. In particular, we show almost sure and $L^p$ convergence for ${\bf M}_{r,N}$, obtain Gaussian fluctuation theorems for ${\bf K}_N$, and establish large deviation principles for both ${\bf K}_N$ and ${\bf M}_{r,N}$. Our approach relies on a random sample size representation of the number of clusters through the corresponding non-hierarchical species sampling model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of clusters in hierarchical species sampling models Favaro, Stefano Feng, Shui Paguyo, J. E. Probability 60F05, 60F10 Consider a sample of size $N$ from a population governed by a hierarchical species sampling model. We study the large $N$ asymptotic behavior of the number ${\bf K}_N$ of clusters and the number ${\bf M}_{r,N}$ of clusters with frequency $r$ in the sample. In particular, we show almost sure and $L^p$ convergence for ${\bf M}_{r,N}$, obtain Gaussian fluctuation theorems for ${\bf K}_N$, and establish large deviation principles for both ${\bf K}_N$ and ${\bf M}_{r,N}$. Our approach relies on a random sample size representation of the number of clusters through the corresponding non-hierarchical species sampling model. |
| title | Asymptotic behavior of clusters in hierarchical species sampling models |
| topic | Probability 60F05, 60F10 |
| url | https://arxiv.org/abs/2501.09741 |