| Summary: | 碩士 === 國立臺灣大學 === 應用數學科學研究所 === 104 === Hidden Markov models are a fundamental tool in applied statistics, econometrics, and machine learning for treating data taken from multiple subpopulations. When the sequence of observations is from a discrete-time, finite-state hidden Markov model, the current practice for estimating the parameters of such models relies on local search heuristics such as the EM algorithm. A new method named as pairing method is proposed to serve as an initial estimate of the transition matrix and parameters in hidden Markov models. Under regularity conditions, it can be shown that EM leads to the maximum likelihood estimator by given a suitable initial estimate. However, there is no method of finding suitable initial points in hidden Markov model. Pairing method can provide a good initial parameter estimate which can expedite EM in terms of computing time.When the underlying state transition matrix is not taken into consideration, the marginal distribution will be
a mixture distribution while only limited information on state transition matrix is kept for inference. In order to recover full information contained in the data on transition matrix, we utilize characteristics of stochastic matrix by enlarging the Markov chain to recover information governing dynamic of transition matrix. Consistent and asymptotic normal estimators of hidden transition matrix are provided.
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