Parametrized Families of Gibbs Measures and their Statistical Inference
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917739686264832 |
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| author | Denker, Manfred Keßeböhmer, Marc Lopes, Artur O. Lopes, Silvia R. C. |
| author_facet | Denker, Manfred Keßeböhmer, Marc Lopes, Artur O. Lopes, Silvia R. C. |
| contents | For Hölder continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $Θ\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_θ= f_0+\sum_{i=1}^d θ_i f_i : θ\in Θ\}$. We show that the maximum likelihood estimator of $θ$ for a family of Gibbs measures with potentials $F_θ$ is consistent and determine its asymptotic distribution under the associated shift-invariant distribution. A second part discusses applications; from confidence intervals through testing problems to connections to Bernoulli distributions and stationary Markov chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametrized Families of Gibbs Measures and their Statistical Inference Denker, Manfred Keßeböhmer, Marc Lopes, Artur O. Lopes, Silvia R. C. Dynamical Systems Statistics Theory 62F02, 62F12, 62E20, 37A50, 37A10 For Hölder continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $Θ\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_θ= f_0+\sum_{i=1}^d θ_i f_i : θ\in Θ\}$. We show that the maximum likelihood estimator of $θ$ for a family of Gibbs measures with potentials $F_θ$ is consistent and determine its asymptotic distribution under the associated shift-invariant distribution. A second part discusses applications; from confidence intervals through testing problems to connections to Bernoulli distributions and stationary Markov chains. |
| title | Parametrized Families of Gibbs Measures and their Statistical Inference |
| topic | Dynamical Systems Statistics Theory 62F02, 62F12, 62E20, 37A50, 37A10 |
| url | https://arxiv.org/abs/2408.01104 |