A Minimum Distance Estimator Approach for Misspecified Ergodic Processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912429909213184 |
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| author | Borodavka, Jaroslav I. Krumscheid, Sebastian Pavliotis, Grigorios A. |
| author_facet | Borodavka, Jaroslav I. Krumscheid, Sebastian Pavliotis, Grigorios A. |
| contents | We propose a minimum distance estimator (MDE) for parameter identification in misspecified models characterized by a sequence of ergodic stochastic processes that converge weakly to the model of interest. The data is generated by the sequence of processes, and we are interested in inferring parameters for the limiting processes. We define a general statistical setting for parameter estimation under such model misspecification and prove the robustness of the MDE. Furthermore, we prove the asymptotic normality of the MDE for multiscale diffusion processes with a well-defined homogenized limit. A tractable numerical implementation of the MDE is provided and realized in the programming language Julia. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_12432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Minimum Distance Estimator Approach for Misspecified Ergodic Processes Borodavka, Jaroslav I. Krumscheid, Sebastian Pavliotis, Grigorios A. Methodology Probability Computation 62F35, 62M20, 60H10, 60F05 We propose a minimum distance estimator (MDE) for parameter identification in misspecified models characterized by a sequence of ergodic stochastic processes that converge weakly to the model of interest. The data is generated by the sequence of processes, and we are interested in inferring parameters for the limiting processes. We define a general statistical setting for parameter estimation under such model misspecification and prove the robustness of the MDE. Furthermore, we prove the asymptotic normality of the MDE for multiscale diffusion processes with a well-defined homogenized limit. A tractable numerical implementation of the MDE is provided and realized in the programming language Julia. |
| title | A Minimum Distance Estimator Approach for Misspecified Ergodic Processes |
| topic | Methodology Probability Computation 62F35, 62M20, 60H10, 60F05 |
| url | https://arxiv.org/abs/2506.12432 |