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Choice of Initial States in Estimating Transition Probabilities of a Finite Ergodic Markov Chain
B. R. Handa
Vol. 59, No. 2 (Aug., 1972), pp. 407-414
Stable URL: http://www.jstor.org/stable/2334585
Page Count: 8
You can always find the topics here!Topics: Transition probabilities, Preliminary estimates, Markov chains, Covariance, Maximum likelihood estimation, Statistical estimation, Ergodic theory, Maximum likelihood estimators, Statistical discrepancies, Logical proofs
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The properties of the maximum likelihood estimators for the transition probabilities in a two-stage ergodic Markov chain depend upon the choice of the initial states. For example, the initial states may be suitably fixed in advance or may be observed from the equilibrium distribution of the chain. A large number of relatively short realizations are assumed available and the asymptotic variances are examined in some detail. The relevant asymptotic covariance matrices are derived also for the s-state chain.
Biometrika © 1972 Biometrika Trust