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

  • Authors:
  • N. Merhav;M. Gutman;J. Ziv

  • Affiliations:
  • Dept. of Electr. Eng., Technion, Haifa;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

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