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Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions

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  • JÖRN DANNEMANN
  • HAJO HOLZMANN

Abstract

. In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non‐standard situations such as testing for zero entries in the transition matrix, one‐sided tests for the parameters of the transition matrix or for the components of the stationary distribution of the underlying Markov chain, or testing boundary restrictions on the parameters of the state‐dependent distributions. In this paper, we briefly discuss how the relevant asymptotic distribution theory for the likelihood ratio test (LRT) when the true parameter is on the boundary extends from the independent and identically distributed situation to HMMs. Then we concentrate on discussing a number of relevant examples. The finite‐sample performance of the LRT in such situations is investigated in a simulation study. An application to series of epileptic seizure counts concludes the paper.

Suggested Citation

  • Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 309-321, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:309-321
    DOI: 10.1111/j.1467-9469.2007.00587.x
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
    3. Paolo Giudici & Tobias Ryden & Pierre Vandekerkhove, 2000. "Likelihood-Ratio Tests for Hidden Markov Models," Biometrics, The International Biometric Society, vol. 56(3), pages 742-747, September.
    4. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178, April.
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    2. Ray, Surajit & Ren, Dan, 2012. "On the upper bound of the number of modes of a multivariate normal mixture," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 41-52.

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