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

Sergey G. Bobkov

doi:10.1007/s00440-017-0756-2

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

Sergey G. Bobkov

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

For sums of independent random variables S_n= X₁+ ⋯ + 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.

Original language	English (US)
Pages (from-to)	229-262
Number of pages	34
Journal	Probability Theory and Related Fields
Volume	170
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-017-0756-2
State	Published - Feb 1 2018

Keywords

Central limit theorem
Coupling
Edgeworth expansions
Transport distances

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abstract = "For sums of independent random variables Sn= X1+ ⋯ + Xn, Berry–Esseen-type bounds are derived for the power transport distances Wp in terms of Lyapunov coefficients Lp + 2. In the case of identically distributed summands, the rates of convergence are refined under Cram{\'e}r{\textquoteright}s condition.",

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