Abstract
It is shown that there does not exist a complete sufficient statistic for the class of allk-state Markov chains,k≧3. Whenk=2 there is a complete sufficient statistic.
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Wright, A.L. Nonexistence of complete sufficient statistics for stationaryk-state Markov chains,k≧3. Ann Inst Stat Math 32, 95–97 (1980). https://doi.org/10.1007/BF02480314
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DOI: https://doi.org/10.1007/BF02480314