Fisher information and the central limit theorem

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

Original languageEnglish (US)
Pages (from-to)1-59
Number of pages59
JournalProbability Theory and Related Fields
Volume159
Issue number1-2
DOIs
StatePublished - Jun 2014

Keywords

  • Central limit theorem
  • Edgeworth-type expansions
  • Entropic distance
  • Entropy

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