2013 Fiscal Year Final Research Report
Developing statistical asymptotic theory for jump processes and its applications
| Project/Area Number |
23740082
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
MASUDA Hiroki 九州大学, マス・フォア・インダストリ研究所, 准教授 (10380669)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 統計的漸近推測 / ジャンプ過程 / 確率過程論 / 確率解析 |
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| Research Abstract |
Mainly, we have derived the following results concerning statistical inference for stochastic process models with jumps: (1) Asymptotic normality of the Gaussian quasi-likelihood type estimator together with an easy-to-use approximate confidence regions, when the model has general non-linear coefficients and non-Gaussian noise; (2) Model-free asymptotic distribution of a bias-corrected functional of residuals, with applications to noise-normality and diffusion-coefficient misspecification tests, when the model is of a general continuous-time regression type; (3) Asymptotic mixed normality of the least-absolute deviation estimator and the quasi-likelihood estimator based on the small-time stable approximation, when the noise process can be approximately non-Gaussian stable in small time. In particular, the proposed estimator in (3) is much more efficient than that in (1), while the model setting in (3) is more limited compared with that of (1).
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Research Products
(33 results)
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[Journal Article] The YUIMA project : A computational framework for simulation and inference of stochastic differential equations2014
Author(s)
Brouste, A., Fukasawa, M., Hino, H., Iacus, S, Kamatani, K., Koike, Y., Masuda, H., Nomura, R., Ogihara, T., Shimuzu, Y., Uchida, M., and Yoshida, N
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Journal Title
Journal of Statistical Software
Volume: 57, no.4
Pages: 1-51
URL
Peer Reviewed
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