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The asymptotics of misspecified MLEs for some stochastic processes: a survey

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  • Yury A. Kutoyants

    (LMM, Le Mans University
    Voronezh State University)

Abstract

This is a review of some recent results on parameter estimation by the continuous time observations for two models of observations. The first one is the so called signal in white Gaussian noise and the second is inhomogeneous Poisson process. The main question in all statements is: what are the properties of the MLE if there is a misspecification in the regularity conditions? We consider three types of regularity: smooth signals, signals with cusp-type singularity and discontinuous signals. We suppose that the statistician assumes one type of regularity/singularity, but the real observations contain signals with different type of singularity/regularity. For example, the theoretical (assumed) model has a discontinuous signal, but the real observed signal has cusp-type singularity. We describe the asymptotic behavior of the MLE in such situations.

Suggested Citation

  • Yury A. Kutoyants, 2017. "The asymptotics of misspecified MLEs for some stochastic processes: a survey," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 347-367, October.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-017-9162-8
    DOI: 10.1007/s11203-017-9162-8
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    References listed on IDEAS

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    1. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
    2. Stigler, Stephen M., 2010. "The Changing History of Robustness," The American Statistician, American Statistical Association, vol. 64(4), pages 277-281.
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    Cited by:

    1. Uehara, Yuma, 2019. "Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4051-4081.
    2. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: cusp case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1137-1157, October.

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