The Annals of Probability

A Berry-Esseen Theorem for Linear Combinations of Order Statistics

R. Helmers

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Abstract

A Berry-Esseen bound of order $n^{-1/2}$ is established for linear combinations of order statistics with smooth weight functions. The underlying distribution function must possess a finite absolute third moment. This improves an earlier result of the author.

Article information

Source
Ann. Probab., Volume 9, Number 2 (1981), 342-347.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994478

Digital Object Identifier
doi:10.1214/aop/1176994478

Mathematical Reviews number (MathSciNet)
MR606999

Zentralblatt MATH identifier
0474.62039

JSTOR
links.jstor.org

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62E20: Asymptotic distribution theory

Keywords
Linear combinations of order statistics Berry-Esseen bounds

Citation

Helmers, R. A Berry-Esseen Theorem for Linear Combinations of Order Statistics. Ann. Probab. 9 (1981), no. 2, 342--347. doi:10.1214/aop/1176994478. https://projecteuclid.org/euclid.aop/1176994478


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