On normal approximation rates for certain sums of dependent random variables

Yosef Rinott

doi:10.1016/0377-0427(94)90016-7

On normal approximation rates for certain sums of dependent random variables

Yosef Rinott^*

^*Corresponding author for this work

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

43 Scopus citations

Abstract

Let X₁, ..., X_n be dependent random variables, and set λ = E∑ⁿ_i=1X_i, and σ² = Var∑ⁿ_i=1X_i. In most of the applications of Stein's method for normal approximations, the error rate |P((∑ⁿ_i=1X_i - 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 language	English
Pages (from-to)	135-143
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	55
Issue number	2
DOIs	https://doi.org/10.1016/0377-0427(94)90016-7
State	Published - 21 Nov 1994
Externally published	Yes

Keywords

Central limit theorem
Dependency graph
Stein's method

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10.1016/0377-0427(94)90016-7

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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.",

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N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Dependency graph

KW - Stein's method

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ER -

On normal approximation rates for certain sums of dependent random variables

Abstract

Keywords

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