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Csiszar's phi-divergences for testing the order in a Markov chain

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Menéndez Calleja, María Luisa and Pardo Llorente, Julio Ángel and Pardo Llorente, Leandro (2001) Csiszar's phi-divergences for testing the order in a Markov chain. Statistical Papers, 42 (3). pp. 313-328. ISSN 0932-5026

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Abstract

Assume that a sequence of observations x(1),...,x(n+r) can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis No that a chain of order r - 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: rho -Divergences. More precisely, if p(a1),...,(ar:ar+1) denotes the transition probability for a r(th) order Markov chain, the hypothesis to be tested is H-0 : p(a1),...,(ar:ar+1) = p(a2),...,(ar):(ar+1), a(i) is an element of {1,...,s}, i = 1,..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic.


Item Type:Article
Uncontrolled Keywords:r th Markov chains, Csiszar's phi-divergences, Statistical Information Theory, goodness of fit tests, divergence statistics.
Subjects:Sciences > Mathematics > Probabilities
ID Code:17554
Deposited On:08 Jan 2013 11:22
Last Modified:26 Jul 2018 07:23

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