## The Annals of Probability

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

R. Helmers

#### 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

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