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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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Official URL: http://www.springerlink.com/content/wtr4a6q9bqftaq6w/fulltext.pdf

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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 |
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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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