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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-6d2048cd-80a3-48e9-9fd6-56f134c67657

Czasopismo

Probability and Mathematical Statistics

Tytuł artykułu

On completeness of random transition counts for Markov chains. II

Autorzy Palma, A. 
Treść / Zawartość http://www.math.uni.wroc.pl/~pms/
Warianty tytułu
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 Wydawnictwo Uniwersytetu Wrocławskiego Sp. z o.o.
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, apalma@math.uni.lodz.pl
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.
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