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On the multi-step MLE-process for ergodic diffusion

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  • Kutoyants, Yu.A.

Abstract

We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion and that there is a learning time interval of the length negligible with respect to the whole time of observations. The preliminary estimator obtained after the learning time is then used in the construction of one-step and two-step MLE processes. We discuss the possibility of the applications of the proposed estimation procedure to several other observations models.

Suggested Citation

  • Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2243-2261
    DOI: 10.1016/j.spa.2016.10.007
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    2. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    3. 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.
    4. 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.
    5. Levanony, David & Shwartz, Adam & Zeitouni, Ofer, 1994. "Recursive identification in continuous-time stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 245-275, February.
    6. Yu. A. Kutoyants & A. Motrunich, 2016. "On multi-step MLE-process for Markov sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 705-724, August.
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    Citations

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    Cited by:

    1. 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.
    2. Kutoyants, Yury A., 2019. "On parameter estimation of the hidden Ornstein–Uhlenbeck process," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 248-263.
    3. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.
    4. Yusuke Kaino & Shogo H. Nakakita & Masayuki Uchida, 2020. "Hybrid estimation for ergodic diffusion processes based on noisy discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 171-198, April.
    5. O. V. Chernoyarov & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: the smooth case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 411-435, May.

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