Markov Chain Order Estimation and Relative Entropy
Abstract
We use the $fdivergence$ 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 arXiv:
 arXiv:0910.0264
 Bibcode:
 2009arXiv0910.0264B
 Keywords:

 Mathematics  Statistics Theory;
 Statistics  Methodology
 EPrint:
 Revised for better and shorter proof, new numerical simulations as well as improved references