IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v216y2025ics0167715224002165.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002165
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110247?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lin, Yiqi & Song, Xinyuan, 2022. "Order selection for regression-based hidden Markov model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. Adam, Timo & Mayr, Andreas & Kneib, Thomas, 2022. "Gradient boosting in Markov-switching generalized additive models for location, scale, and shape," Econometrics and Statistics, Elsevier, vol. 22(C), pages 3-16.
    3. Tardy, Olivia & Lenglos, Christophe & Lai, Sandra & Berteaux, Dominique & Leighton, Patrick A., 2023. "Rabies transmission in the Arctic: An agent-based model reveals the effects of broad-scale movement strategies on contact risk between Arctic foxes," Ecological Modelling, Elsevier, vol. 476(C).
    4. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    5. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    6. Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    7. Fulvia Pennoni & Francesco Bartolucci & Silvia Pandolfi, 2024. "Variable Selection for Hidden Markov Models with Continuous Variables and Missing Data," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 568-589, November.
    8. Mevin B. Hooten & Ruth King & Roland Langrock, 2017. "Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 224-231, September.
    9. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
    10. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 457-485, June.
    11. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    12. Ting Wang & Jiancang Zhuang & Kazushige Obara & Hiroshi Tsuruoka, 2017. "Hidden Markov modelling of sparse time series from non-volcanic tremor observations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 691-715, August.
    13. Derek S. Young & Xi Chen & Dilrukshi C. Hewage & Ricardo Nilo-Poyanco, 2019. "Finite mixture-of-gamma distributions: estimation, inference, and model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1053-1082, December.
    14. Roland Langrock & Thomas Kneib & Alexander Sohn & Stacy L. DeRuiter, 2015. "Nonparametric inference in hidden Markov models using P-splines," Biometrics, The International Biometric Society, vol. 71(2), pages 520-528, June.
    15. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    16. 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.
    17. Zhou, Jie & Song, Xinyuan & Sun, Liuquan, 2020. "Continuous time hidden Markov model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    18. Baolin Wu, 2013. "Sparse cluster analysis of large-scale discrete variables with application to single nucleotide polymorphism data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 358-367, February.
    19. Floriane Cardiec & Sophie Bertrand & Matthew J Witt & Kristian Metcalfe & Brendan J Godley & Catherine McClellan & Raul Vilela & Richard J Parnell & François le Loc’h, 2020. "“Too Big To Ignore”: A feasibility analysis of detecting fishing events in Gabonese small-scale fisheries," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    20. Henryk Gurgul & Robert Syrek & Christoph Mitterer, 2016. "Price duration versus trading volume in high-frequency data for selected DAX companies," Managerial Economics, AGH University of Science and Technology, Faculty of Management, vol. 17(2), pages 241-260.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.