Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for 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 Cramér’s condition.

Original languageEnglish (US)
Pages (from-to)229-262
Number of pages34
JournalProbability Theory and Related Fields
Volume170
Issue number1-2
DOIs
StatePublished - Feb 1 2018

Keywords

  • Central limit theorem
  • Coupling
  • Edgeworth expansions
  • Transport distances

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