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December, 1977 The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions
R. Helmers
Ann. Probab. 5(6): 940-953 (December, 1977). DOI: 10.1214/aop/1176995662

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.

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R. Helmers. "The Order of the Normal Approximation for Linear Combinations of Order Statistics with Smooth Weight Functions." Ann. Probab. 5 (6) 940 - 953, December, 1977. https://doi.org/10.1214/aop/1176995662

Information

Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0373.62026
MathSciNet: MR458716
Digital Object Identifier: 10.1214/aop/1176995662

Subjects:
Primary: 62G30
Secondary: 62E20

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 6 • December, 1977
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