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arXiv · 2408.01104

Parametrized Families of Gibbs Measures and their Statistical Inference

Manfred Denker·Marc Keßeböhmer·Artur O. Lopes·Silvia R. C. Lopes
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Abstract

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.

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Manfred Denker, Marc Keßeböhmer, Artur O. Lopes, Silvia R. C. Lopes. 2024-08-02. Parametrized Families of Gibbs Measures and their Statistical Inference. https://arxiv.org/abs/2408.01104

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