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Choice of Initial States in Estimating Transition Probabilities of a Finite Ergodic Markov Chain

B. R. Handa
Biometrika
Vol. 59, No. 2 (Aug., 1972), pp. 407-414
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334585
Stable URL: http://www.jstor.org/stable/2334585
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Choice of Initial States in Estimating Transition Probabilities of a Finite Ergodic Markov Chain
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Abstract

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.

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