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On multi-step MLE-process for Markov sequences

Author

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  • Yu. A. Kutoyants

    (Université du Maine
    National Research University “MPEI”)

  • A. Motrunich

    (Université du Maine
    Statésia)

Abstract

We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:6:d:10.1007_s00184-015-0574-4
    DOI: 10.1007/s00184-015-0574-4
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    References listed on IDEAS

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    1. Yosihiko Ogata & Nobuo Inagaki, 1977. "The weak convergence of the likelihood ratio random fields for Markov observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 165-187, December.
    2. 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. 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.
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