Robust estimation for order of hidden Markov models based on density power divergences

• Published in: Journal of statistical computation and simulation Vol. 80; no. 5; pp. 503 - 512
• Main Authors: Lee, Sangyeol, Lee, Taewook
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.05.2010; Taylor & Francis Ltd
• Subjects: Asymptotic methods; Asymptotic properties; Computer simulation; Conics; Density; Divergence; Estimating techniques; Estimators; hidden Markov model; Markov analysis; Mathematical analysis; Mathematical models; minimum density power divergence estimator; non-identifiable model; Parameter estimation; robust estimator; Statistical inference; Stochastic models
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650902725155

In this paper, we study the robust estimation for the order of hidden Markov model (HMM) based on a penalized minimum density power divergence estimator, which is obtained by utilizing the finite mixture marginal distribution of HMM. For this task, we adopt the locally conic parametrization method used in [D. Dacunha-Castelle and E. Gassiate, Testing in locally conic models and application to mixture models. ESAIM Probab. Stat. (1997), pp. 285-317; D. Dacunha-Castelle and E. Gassiate, Testing the order of a model using locally conic parametrization: population mixtures and stationary arma processes, Ann. Statist. 27 (1999), pp. 1178-1209; T. Lee and S. Lee, Robust and consistent estimation of the order of finite mixture models based on the minimizing a density power divergence estimator, Metrika 68 (2008), pp. 365-390] to avoid the difficulties that arise in handling mixture marginal models, such as the non-identifiability of the parameter space and the singularity problem with the asymptotic variance. We verify that the estimated order is consistent and simulation results are provided for illustration.