On estimating the memory for finitarily Markovian processes

Gusztáv Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Finitarily Markovian processes are those processes {Xn}n = - ∞ for which there is a finite K (K = K ({Xn}n = - ∞0)) such that the conditional distribution of X1 given the entire past is equal to the conditional distribution of X1 given only {Xn}n = 1 - K0. The least such value of K is called the memory length. We give a rather complete analysis of the problems of universally estimating the least such value of K, both in the backward sense that we have just described and in the forward sense, where one observes successive values of {Xn} for n ≥ 0 and asks for the least value K such that the conditional distribution of Xn + 1 given {Xi}i = n - K + 1n is the same as the conditional distribution of Xn + 1 given {Xi}i = - ∞n. We allow for finite or countably infinite alphabet size.

Original languageEnglish
Pages (from-to)15-30
Number of pages16
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume43
Issue number1
DOIs
Publication statusPublished - Jan 1 2007

Keywords

  • Nonparametric estimation
  • Stationary processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'On estimating the memory for finitarily Markovian processes'. Together they form a unique fingerprint.

  • Cite this