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 language||English (US)|
|Number of pages||59|
|Journal||Probability Theory and Related Fields|
|State||Published - Jun 2014|
Bibliographical noteFunding Information:
Research partially supported by NSF grant DMS-1106530 and SFB 701.
- Central limit theorem
- Edgeworth-type expansions
- Entropic distance