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On the estimation of the order of a Markov chain and universal data compression

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3 Author(s)
N. Merhav ; Dept. of Electr. Eng., Technion, Haifa, Israel ; M. Gutman ; J. Ziv

The authors estimate the order of a finite Markov source based on empirically observed statistics. The performance criterion adopted is to minimize the probability of underestimating the model order while keeping the overestimation probability exponent at a prescribed level. A universal asymptotically optimal test, in the sense just defined, is proposed for the case where a given integer is known to be the upper bound of the true order. For the case where such a bound is unavailable, an alternative rule based on the Lempel-Ziv data compression algorithm is shown to be asymptotically optimal also and computationally more efficient

Published in:

IEEE Transactions on Information Theory  (Volume:35 ,  Issue: 5 )