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Abstract Details
Activity Number:
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352
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract - #302393 |
Title:
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Asymptotics of Markov Order Estimators for Infinite Memory Processes
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Author(s):
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Zsolt Talata*+
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Companies:
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University of Kansas
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Address:
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Department of Mathematics, Lawrence, KS, 66045-7523,
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Keywords:
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Markov order estimator ;
information criterion ;
divergence rate ;
asymptotics ;
ergodic process ;
infinite memory
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Abstract:
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For finite-alphabet stationary ergodic processes with infinite memory, Markov order estimators that optimize an information criterion over the candidate orders based on a sample of size n are investigated. Three familiar information criteria are considered: the Bayesian information criterion (BIC) with generalized penalty term yielding the penalized maximum likelihood (PML), and the normalized maximum likelihood (NML) and the Krichevsky-Trofimov (KT) code lengths. A bound on the probability that the estimated order is greater than some order is obtained under the assumption that the process is weakly non-null and alpha-summable. This gives an O(log n) upper bound on the estimated order eventually almost surely as n tends to infinity. Moreover, a bound on the probability that the estimated order is less than some order is obtained if the decay of the continuity rate of the weakly non-null process is in some exponential range. This implies that then the estimated order attains the O(log n) divergence rate eventually almost surely as n tends to infinity.
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