Robust estimation via $γ$-divergence for diffusion processes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918371229958144 |
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| author | Nakagawa, Tomoyuki Shimizu, Yusuke |
| author_facet | Nakagawa, Tomoyuki Shimizu, Yusuke |
| contents | This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $γ$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust estimation via $γ$-divergence for diffusion processes Nakagawa, Tomoyuki Shimizu, Yusuke Methodology Statistics Theory 62F35, 60J60 This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $γ$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness. |
| title | Robust estimation via $γ$-divergence for diffusion processes |
| topic | Methodology Statistics Theory 62F35, 60J60 |
| url | https://arxiv.org/abs/2603.04752 |