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

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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.

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Acknowledgements

I would like to thank the Reviewer for the careful reading this manuscript and several useful advices. This work was done under partial financial support of the grant RSF number 15-11-10022.

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Authors and Affiliations

  1. LMM, Le Mans University, Le Mans, France

    Yury A. Kutoyants

  2. Voronezh State University, Voronezh, Russia

    Yury A. Kutoyants

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  1. Yury A. Kutoyants
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Correspondence to Yury A. Kutoyants.

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Kutoyants, Y.A. The asymptotics of misspecified MLEs for some stochastic processes: a survey. Stat Inference Stoch Process 20, 347–367 (2017). https://doi.org/10.1007/s11203-017-9162-8

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  • DOI: https://doi.org/10.1007/s11203-017-9162-8

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