Balanced importance resampling for Markov chains

C. D. Fuh, T. H. Fan, W. L. Hung

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, given a sequence of realizations of a discrete-time finite state Markov chain, we estimate both transition probabilities and invariant distributions using a bootstrap method. In its original form this technique requires independent and identically distributed samples. Therefore, since the sequence is "Markov", it has to be adapted in order to fit into this framework. Block bootstrap is introduced to make this adaptation. In order to reduce computer time, balanced importance resampling is proposed, so that in the bootstrap procedure, resampling is not done uniformly, this distribution is modified in order to get variance reduction. Efficiency properties of this alternative distribution are shown, together with numerical data. A central limit theorem for multinomial random sums is also proved.

Original languageEnglish
Pages (from-to)221-241
Number of pages21
JournalJournal of Statistical Planning and Inference
Volume83
Issue number1
DOIs
StatePublished - 1 Jan 2000

Keywords

  • Balanced importance resampling
  • Bootstrap
  • Invariant distribution
  • Markov chains
  • Primary 62G05
  • Secondary 60F05
  • Transition probability

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