Interaction Order Estimation in Tensor Curie-Weiss Models
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910670972256256 |
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| author | Mukherjee, Somabha |
| author_facet | Mukherjee, Somabha |
| contents | In this paper, we consider the problem of estimating the interaction parameter $p$ of a $p$-spin Curie-Weiss model at inverse temperature $β$, given a single observation from this model. We show, by a contiguity argument, that joint estimation of the parameters $β$ and $p$ is impossible, which implies that estimation of $p$ is impossible if $β$ is unknown. These impossibility results are also extended to the more general $p$-spin Erdős-Rényi Ising model. The situation is more delicate when $β$ is known. In this case, we show that there exists an increasing threshold function $β^*(p)$, such that for all $β$, consistent estimation of $p$ is impossible when $β^*(p) > β$, and for almost all $β$, consistent estimation of $p$ is possible for $β^*(p)<β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interaction Order Estimation in Tensor Curie-Weiss Models Mukherjee, Somabha Statistics Theory Probability In this paper, we consider the problem of estimating the interaction parameter $p$ of a $p$-spin Curie-Weiss model at inverse temperature $β$, given a single observation from this model. We show, by a contiguity argument, that joint estimation of the parameters $β$ and $p$ is impossible, which implies that estimation of $p$ is impossible if $β$ is unknown. These impossibility results are also extended to the more general $p$-spin Erdős-Rényi Ising model. The situation is more delicate when $β$ is known. In this case, we show that there exists an increasing threshold function $β^*(p)$, such that for all $β$, consistent estimation of $p$ is impossible when $β^*(p) > β$, and for almost all $β$, consistent estimation of $p$ is possible for $β^*(p)<β$. |
| title | Interaction Order Estimation in Tensor Curie-Weiss Models |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2410.20213 |