Csiszar’s ?-divergences for testing the order in a Markov chain |
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Authors: | M L Menéndez J A Pardo L Pardo |
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Institution: | (1) Department of Applied Mathematics, E.T.S.A.M., Technical University of Madrid, 28040 Madrid, Spain, ES;(2) Department of Statistics & O.R., Complutense University of Madrid, 28040 Madrid, Spain, ES |
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Abstract: | 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 H
0 that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: ϕ-Divergences. More precisely, if p
a
1 .....,
a
r:
a
r
+1 denotes the transition probability for a r
th
order Markov chain, the hypothesis to be tested is
H
0:p
a
1 .....,
a
r:
a
r
+1 = p
a
2 .....,
a
r:
a
r
+1, a
i
∈{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.
Received: August 3, 1998; revised version: November 25, 1999 |
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Keywords: | and phrases:rth Markov chains Csiszar's ϕ -divergences Statistical Information Theory goodness of fit tests divergence statistics |
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