Parametrized Families of Gibbs Measures and their Statistical Inference
| Autor: | Denker, Manfred, Keßeböhmer, Marc, Lopes, Artur O., Lopes, Silvia R. C. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$. We show that the maximum likelihood estimator of $\theta$ for a family of Gibbs measures with potentials $F_\theta$ 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. Comment: 37 pages |
| Databáze: | arXiv |
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