Consistent Estimation of Partition Markov Models
Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Maxim Raginsky
Received: 1 March 2017 / Revised: 31 March 2017 / Accepted: 4 April 2017 / Published: 6 April 2017
The Partition Markov Model characterizes the process by a partition
of the state space, where the elements in each part of
share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n
realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n
goes to infinity,
will be retrieved. We show an application to model internet navigation patterns.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
García, J.E.; González-López, V.A. Consistent Estimation of Partition Markov Models. Entropy 2017, 19, 160.
García JE, González-López VA. Consistent Estimation of Partition Markov Models. Entropy. 2017; 19(4):160.
García, Jesús E.; González-López, Verónica A. 2017. "Consistent Estimation of Partition Markov Models." Entropy 19, no. 4: 160.
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