On normal approximation rates for certain sums of dependent random variables

Yosef Rinott*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

Let X1, ..., Xn be dependent random variables, and set λ = E∑ni=1Xi, and σ2 = Var∑ni=1Xi. In most of the applications of Stein's method for normal approximations, the error rate |P((∑ni=1Xi - λ)/σ ≤ w) - Φ(w)| is of the order of σ- 1 2. This rate was improved by Stein (1986) and others in some special cases. In this paper it is shown that for certain bounded random variables, a simple refinement of error-term calculations in Stein's method leads to improved rates.

Original languageEnglish
Pages (from-to)135-143
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume55
Issue number2
DOIs
StatePublished - 21 Nov 1994
Externally publishedYes

Keywords

  • Central limit theorem
  • Dependency graph
  • Stein's method

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