Consistent Estimation of Partition Markov Models

The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L 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, L will be retrieved. We show an application to model internet navigation patterns.

• Publication year

  2017

• Venue

  Entropy

• Publication date

  2017-04-06

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.3390/e19040160
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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