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Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise

Author

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  • Shogo H. Nakakita

    (Osaka University)

  • Yusuke Kaino

    (Osaka University)

  • Masayuki Uchida

    (Osaka University)

Abstract

We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and drift parameters are introduced and the polynomial-type large deviation inequalities for those quasi-likelihoods are shown to see the asymptotic properties of the adaptive Bayes-type estimators and the convergence of moments for both adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones.

Suggested Citation

  • Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-020-00746-3
    DOI: 10.1007/s10463-020-00746-3
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
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    5. Masayuki Uchida & Nakahiro Yoshida, 2014. "Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 181-219, July.
    6. Ilia Negri & Yoichi Nishiyama, 2017. "Moment convergence of Z-estimators," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 387-397, October.
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    8. Shogo H. Nakakita & Masayuki Uchida, 2019. "Inference for ergodic diffusions plus noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 470-516, June.
    9. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    10. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
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    Cited by:

    1. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.

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