RATE OF CONVERGENCE AND EDGEWORTH-TYPE EXPANSION IN THE ENTROPIC CENTRAL LIMIT THEOREM

RATE OF CONVERGENCE AND EDGEWORTH-TYPE EXPANSION IN THE ENTROPIC CENTRAL LIMIT THEOREM

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.

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Bibliographische Detailangaben
Veröffentlicht in:The Annals of probability 2013-07, Vol.41 (4), p.2479-2512
Hauptverfasser: Bobkov, Sergey G., Chistyakov, Gennadiy P., Götze, Friedrich
Format: Artikel
Sprache:eng
Schlagworte:
60E
Central limit theorem
Covariance matrices
Edgeworth-type expansions
entropic distance
Entropy
Integers
Log integral function
Mathematical moments
Mathematical theorems
Normal distribution
Perceptron convergence procedure
Polynomials
Random variables
Studies
Topology
Vector space
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Beschreibung
Zusammenfassung:An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
ISSN:0091-1798
2168-894X
DOI:10.1214/12-aop780