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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 32, Fasc. 2,
pages 203 - 214
 

ON COMPLETENESS OF RANDOM TRANSITION COUNTS FOR MARKOV CHAINS. II

Agnieszka Palma

Abstract: 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].

2000 AMS Mathematics Subject Classification: 62B05.

Keywords and phrases: Markov chain, random transition count, minimal sufficient statistic, complete statistic.

References

[1]   J. L. Denny and A. L. Wright, On tests for Markov dependence, Z. Wahrsch. Verw. Gebie-te 43 (1978), pp. 331–338.

[2]   J. L. Denny and S. J. Yakowitz, Admissible run-contingency type tests for independence and Markov dependence, J. Amer. Statist. Assoc. 73 (1978), pp. 177–181.

[3]   E. L. Lehmann, Testing Statistical Hypotheses, Wiley, New York 1986.

[4]   E. L. Lehmann and H. Scheffé, Completeness, similar regions, and unbiased estimation. Part I, Sankhya 10 (1950), pp. 305–340. Completeness, similar regions, and unbiased estimation. Part II, Sankhya 15 (1955), pp. 219–236.

[5]   A. Palma, On completeness of random transition count for Markov chains, J. Appl. Anal. 12 (2006), pp. 249–258.

[6]   A. Paszkiewicz, When transition count for Markov chains is a complete sufficient statistic, Statist. Probab. Lett. 76 (2006), pp. 757–763.

[7]   M. J. Schervish, Theory of Statistics, Springer, New York 1995.

[8]   A. L. Wright, Nonexistence of complete sufficient statistics for stationary k -state Markov chains, k ≠ 3, Ann. Inst. Statist. Math. 32 (1980), pp. 95–97.

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