Estimating the lengths of memory words

Guszt́v Morvai*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

For a stationary stochastic process {Xn} with values in some set A, a finite word w ∈ AK is called a memory word if the conditional probability of X0 given the past is constant on the cylinder set defined by X-K-1 = w. It is a called a minimal memory word if no proper suffix of w is also a memory word. For example in a K-step Markov processes all words of length K are memory words but not necessarily minimal. We consider the problem of determining the lengths of the longest minimal memory words and the shortest memory words of an unknown process {X n} based on sequentially observing the outputs of a single sample {ξ1, ξ2...ξn}. We will give a universal estimator which converges almost surely to the length of the longest minimal memory word and show that no such universal estimator exists for the length of the shortest memory word. The alphabet A may be finite or countable.

Original languageEnglish
Pages (from-to)3804-3807
Number of pages4
JournalIEEE Transactions on Information Theory
Volume54
Issue number8
DOIs
StatePublished - Aug 2008

Keywords

  • Markov chains
  • Order estimation
  • Probability
  • Stationary processes
  • Statistics
  • Stochastic processes

Fingerprint

Dive into the research topics of 'Estimating the lengths of memory words'. Together they form a unique fingerprint.

Cite this