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Fisher information and the central limit theorem. (English) Zbl 1372.60018
The authors establish an Edgeworth-type expansion for the relative Fisher information distance between normal distributions and sums of independent identically distributed random variables, satisfying moment conditions. To this end, general properties of densities with finite Fisher information are considered, as well as Fisher information as a functional and classes of densities represented as convolutions. Validity of the central limit theorem is studied under conditions related to Fisher information and convolutions.

MSC:
60F05 Central limit and other weak theorems
94A17 Measures of information, entropy
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