Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances

For sums of independent random variables S n = X 1 + ⋯ + X n , Berry–Esseen-type bounds are derived for the power transport distances W p in terms of Lyapunov coefficients L p + 2 . In the case of identically distributed summands, the rates of convergence are refined under Cramér’s condition.

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Bibliographic Details
Published in:Probability theory and related fields 2018-02, Vol.170 (1-2), p.229-262
Main Author: Bobkov, Sergey G.
Format: Article
Language:English
Subjects:
Central limit theorem
Economics
Finance
Independent variables
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Statistics for Business
Theoretical
Transport
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Description
Summary:For sums of independent random variables S n = X 1 + ⋯ + X n , Berry–Esseen-type bounds are derived for the power transport distances W p in terms of Lyapunov coefficients L p + 2 . In the case of identically distributed summands, the rates of convergence are refined under Cramér’s condition.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-017-0756-2