Markov Chain Order Estimation and Relative Entropy

Details Markov Chain Order Estimation and Relative Entropy Markov Chain Order Estimation and Relative Entropy

2009-10-01

arxiv.org/abs/0910.0264v4

Mathematics

Statistics Theory

Revised for better and shorter proof, new numerical simulations as well as improved references

Scientific paper

We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a Markov Chain to be used in the definition of a couple of estimators i.e. the Local Dependency Level and Global Dependency Level for a Markov chain sample. After exploring their properties we propose a new estimator for the Markov chain order. Finally we show a few tables containing numerical simulation results, comparing the performance of the new estimator with the well known and already established AIC and BIC estimators.

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