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Penalized composite likelihood estimation for hidden Markov models with unknown number of states

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  • Lin, Yong
  • Huang, Mian

Abstract

Estimating hidden Markov models (HMMs) with unknown number of states is a challenging task. In this paper, we propose a new penalized composite likelihood approach for simultaneously estimating both the number of states and the parameters in an overfitted HMM. We prove the order selection consistency and asymptotic normality of the resultant estimator. Simulation studies and an application demonstrate the finite sample performance of the proposed method.

Suggested Citation

  • Lin, Yong & Huang, Mian, 2025. "Penalized composite likelihood estimation for hidden Markov models with unknown number of states," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002165
    DOI: 10.1016/j.spl.2024.110247
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    References listed on IDEAS

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    1. Lin, Yiqi & Song, Xinyuan, 2022. "Order selection for regression-based hidden Markov model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    3. Chen, Jiahua & Khalili, Abbas, 2009. "Order Selection in Finite Mixture Models With a Nonsmooth Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 187-196.
    4. Ying Hung & Yijie Wang & Veronika Zarnitsyna & Cheng Zhu & C. F. Jeff Wu, 2013. "Hidden Markov Models With Applications in Cell Adhesion Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1469-1479, December.
    5. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
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