On the constant in the nonuniform version of the Berry-Esséen theorem

  • R. Michel
Article

DOI: 10.1007/BF01013464

Cite this article as:
Michel, R. Z. Wahrscheinlichkeitstheorie verw Gebiete (1981) 55: 109. doi:10.1007/BF01013464

Summary

LetX1,X2,⋯ be a sequence of independent and identically distributed random variables withEX1=0 andEX12=1. It is shown that for allnℕ∈ and allt∈ℝ,
$$\left| {P\left( {n^{ - 1/2} \sum\limits_{i = 1}^n {X_i< t} } \right) - \Phi (t)} \right| \leqq c_{\text{1}} n^{ - 1/2} E|X_1 |^3 (1 + |t|^3 )^{ - 1}$$
wherec1c0+8(1+e) (c0 being the constant in the Berry-Esséen Theorem.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • R. Michel
    • 1
  1. 1.Fachbereich 7 - MathematikUniversität - Gesamthochschule - WuppertalWuppertal 1Federal Republic of Germany