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Brouste A, Farinetto C. Fast and asymptotically efficient estimation in the Hawkes processes. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2023. [DOI: 10.1007/s42081-023-00186-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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Tonaki Y, Uchida M. Change point inference in ergodic diffusion processes based on high frequency data. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.12.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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3
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Quasi-likelihood analysis and its applications. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2022. [DOI: 10.1007/s11203-021-09266-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
AbstractThe Ibragimov–Khasminskii theory established a scheme that gives asymptotic properties of the likelihood estimators through the convergence of the likelihood ratio random field. This scheme is extending to various nonlinear stochastic processes, combined with a polynomial type large deviation inequality proved for a general locally asymptotically quadratic quasi-likelihood random field. We give an overview of the quasi-likelihood analysis and its applications to ergodic/non-ergodic statistics for stochastic processes.
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Tonaki Y, Kaino Y, Uchida M. Estimation for change point of discretely observed ergodic diffusion processes. Scand Stat Theory Appl 2022. [DOI: 10.1111/sjos.12567] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Affiliation(s)
- Yozo Tonaki
- Graduate School of Engineering Science, Osaka University, 1‐3, Machikaneyama, Toyonaka Osaka Japan
| | - Yusuke Kaino
- Graduate School of Maritime Sciences, Kobe University, 5‐1‐1, Fukaeminami‐machi, Higashinada‐ku Kobe Japan
| | - Masayuki Uchida
- Graduate School of Engineering Science, and Center for Mathematical Modeling and Date Science, Osaka University, 1‐3, Machikaneyama, Toyonaka, Osaka, 560‐8531, Japan; Center for Mathematical Modeling and Data Science (MMDS), Osaka University Toyanaka Japan
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Masuda H, Uehara Y. Estimating diffusion with compound Poisson jumps based on self-normalized residuals. J Stat Plan Inference 2021. [DOI: 10.1016/j.jspi.2021.02.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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6
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Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2021. [DOI: 10.1007/s11203-021-09249-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Kaino Y, Uchida M. Parametric estimation for a parabolic linear SPDE model based on discrete observations. J Stat Plan Inference 2021. [DOI: 10.1016/j.jspi.2020.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Affiliation(s)
- Arnaud Gloter
- Université Paris-Saclay, CNRS, Univ Evry, Laboratoire de Mathématiques et Modélisation d’Evry, 91037, Evry-Courcouronnes, France
| | - Nakahiro Yoshida
- Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan https://www.ms.u-tokyo.ac.jp/~nakahiro/hp-naka-e
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Kutoyants YA, Zhou L. On parameter estimation of the hidden Gaussian process in perturbed SDE. Electron J Stat 2021. [DOI: 10.1214/20-ejs1788] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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11
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Regularized bridge-type estimation with multiple penalties. ANN I STAT MATH 2020. [DOI: 10.1007/s10463-020-00769-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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12
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Nakakita SH, Kaino Y, Uchida M. Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise. ANN I STAT MATH 2020. [DOI: 10.1007/s10463-020-00746-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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13
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Penalized least squares approximation methods and their applications to stochastic processes. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2020. [DOI: 10.1007/s42081-019-00064-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Kaino Y, Nakakita SH, Uchida M. Hybrid estimation for ergodic diffusion processes based on noisy discrete observations. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2019. [DOI: 10.1007/s11203-019-09203-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Data driven time scale in Gaussian quasi-likelihood inference. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2019. [DOI: 10.1007/s11203-019-09197-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Kutoyants YA. On parameter estimation of hidden ergodic Ornstein-Uhlenbeck process. Electron J Stat 2019. [DOI: 10.1214/19-ejs1631] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Kamatani K. Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution. BERNOULLI 2018. [DOI: 10.3150/17-bej976] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Kaino Y, Uchida M. Hybrid estimators for stochastic differential equations from reduced data. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2018. [DOI: 10.1007/s11203-018-9184-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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22
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De Gregorio A, Iacus SM. Empirical
$$L^2$$
L
2
-distance test statistics for ergodic diffusions. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2018. [DOI: 10.1007/s11203-018-9176-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Abstract
Abstract
We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.
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