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Hybrid estimators for stochastic differential equations from reduced data

Author

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  • Yusuke Kaino

    (Osaka University)

  • Masayuki Uchida

    (Osaka University
    Osaka University)

Abstract

We treat parametric inference for unknown parameters of stochastic differential equations from discrete observations from the viewpoint of computational cost. Following Kamatani et al. (Bull Inf Cybern 48:19–35, 2016) and Kaino and Uchida (Hybrid estimators for ergodic diffusion processes from thinned data, 2018), we present the asymptotic results of the multi-step estimators with the initial Bayes type estimators for both ergodic and non-ergodic diffusion type processes. The initial Bayes type estimators are constructed by means of both the reduced data and the thinned data obtained from the full data. Some examples and simulation results are also given.

Suggested Citation

  • Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for stochastic differential equations from reduced data," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 435-454, July.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9184-x
    DOI: 10.1007/s11203-018-9184-x
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    References listed on IDEAS

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    Cited by:

    1. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.
    2. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2023. "Estimation for change point of discretely observed ergodic diffusion processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 142-183, March.
    3. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.

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