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On completeness of random transition counts for Markov chains. II

Palma A.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 2

203--214

It is shown that the random transition count is complete for Markov chains with a fixed length and a fixed initial state, for some subsets of the set of all transition probabilities. The main idea is to apply graph theory to prove completeness in a more general case than in Palma [5].

On completeness of random transition count for Markov chains

Palma A.

Journal of Applied Analysis

2006

Vol. 12, nr 2

249-258

It is shown that the random transition count is complete for Markov chains with a fixed lenght and a fixed lenght and a fixed initial state, for some subsets of the set of all transition probabilities.

On minimal pairwise sufficient statistic

Kuśmierek A.

Journal of Applied Analysis

2001

Vol. 7, nr 2

285-292

Each statistic, which is pairwise sufficient and (in a natural sense) countably complete, is a minimal pairwise sufficient statistic. The Basu theorem for pairwise sufficient statistic is also obtained.