The Annals of Probability

The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions

R. Helmers

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Abstract

A Berry-Esseen bound of order $n^{-\frac{1}{2}}$ is established for linear combinations of order statistics. The theorem requires a "smooth" weight function, and the underlying distribution function must not have "too much weight in the tails." The distribution function need not be continuous.

Article information

Source
Ann. Probab., Volume 5, Number 6 (1977), 940-953.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995662

Digital Object Identifier
doi:10.1214/aop/1176995662

Mathematical Reviews number (MathSciNet)
MR458716

Zentralblatt MATH identifier
0373.62026

JSTOR
links.jstor.org

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

Keywords
Linear combinations of order statistics order of normal approximation

Citation

Helmers, R. The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions. Ann. Probab. 5 (1977), no. 6, 940--953. doi:10.1214/aop/1176995662. https://projecteuclid.org/euclid.aop/1176995662


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