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Nonasymptotic control of the MLE for misspecified nonparametric hidden Markov models

Abstract : Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states. We consider the problem of estimating an unknown process distribution using nonparametric hidden Markov models in the misspecified setting, that is when the data-generating process may not be a hidden Markov model. We show that when the true distribution is exponentially mixing and satisfies a forgetting assumption, the maximum likelihood estimator recovers the best approximation of the true distribution. We prove a finite sample bound on the resulting error and show that it is optimal in the minimax sense--up to logarithmic factors--when the model is well specified.
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https://hal.archives-ouvertes.fr/hal-01833274
Contributor : Luc Lehéricy <>
Submitted on : Friday, February 12, 2021 - 12:29:53 PM
Last modification on : Tuesday, February 16, 2021 - 3:20:17 AM

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Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License

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  • HAL Id : hal-01833274, version 2
  • ARXIV : 1807.03997

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Luc Lehéricy. Nonasymptotic control of the MLE for misspecified nonparametric hidden Markov models. 2018. ⟨hal-01833274v2⟩

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