The Annals of Probability

On Normal Approximations of Distributions in Terms of Dependency Graphs

Pierre Baldi and Yosef Rinott

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Abstract

Bounds on the error in the normal approximation of sums of dependent random variables introduced by Stein are interpreted in terms of dependency graphs. This leads to improvements on a central limit theorem of Petrovskaya and Leontovich and recent applications by Baldi and Rinott. In particular, bounds on rates of convergence are obtained. As an application we study the normal approximation to the number of local maxima of a random function on a graph.

Article information

Source
Ann. Probab. Volume 17, Number 4 (1989), 1646-1650.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176991178

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176991178

Mathematical Reviews number (MathSciNet)
MR1048950

Zentralblatt MATH identifier
0691.60020

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 05C99: None of the above, but in this section

Keywords
Central limit theorem dependent variables rates of convergence random local maxima

Citation

Baldi, Pierre; Rinott, Yosef. On Normal Approximations of Distributions in Terms of Dependency Graphs. The Annals of Probability 17 (1989), no. 4, 1646--1650. doi:10.1214/aop/1176991178. http://projecteuclid.org/euclid.aop/1176991178.


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