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Two new Markov order estimators

Research paper by Yuval Peres, Paul Shields

Indexed on: 04 Jun '05Published on: 04 Jun '05Published in: Mathematics - Statistics



Abstract

We present two new methods for estimating the order (memory depth) of a finite alphabet Markov chain from observation of a sample path. One method is based on entropy estimation via recurrence times of patterns, and the other relies on a comparison of empirical conditional probabilities. The key to both methods is a qualitative change that occurs when a parameter (a candidate for the order) passes the true order. We also present extensions to order estimation for Markov random fields.