On completeness of random transition counts for Markov chains. II

• Autorzy: Palma A.
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Markov chain; random transition count; minimal sufficient statistic; complete statistic

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2012
• Tom: Vol. 32, Fasc. 2
• Strony: 203--214
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Palma A.

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] J. L. Denny and A. L. Wright, On tests for Markov dependence, Z. Wahrsch. Verw. Gebiete 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.