Fisher information and the central limit theorem

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

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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
Issue number1-2
StatePublished - Jun 2014

Bibliographical note

Funding Information:
Research partially supported by NSF grant DMS-1106530 and SFB 701.


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


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