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Biometrika 1976 63(1):211-213; doi:10.1093/biomet/63.1.211
© 1976 by Biometrika Trust
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Miscellanea

Statistical inference for Markov chains with lumped states

A. SHAIKH

Department of Statistics and Operational Research, Brunel University Uxbridge, Middlesex

In an (n+1)-state homogeneous Markov chain, when due to some experimental limitations n states are not observable, the maximum likelihood estimation of an unknown parameter {theta} is considered and the efficiency of {theta} relative to the most efficient estimator when all the states are observable is discussed. The study is extended to the case when there are two lumps of unobservable states in a four-state Markov chain.

Key Words: Efficiency of estimation • First return time probability • Lumped states • Markov chain • Probability generating function


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