## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 2 (1977), 357-369.

### Error Bounds for Linear Combinations of Order Statistics

#### Abstract

A Berry-Esseen bound is obtained for trimmed linear combinations of order statistics. These linear combinations are written as the sum of a linear and a quadratic combination of independent exponentially distributed random variables plus a remainder term. The remainder term is shown to be of negligible order and Fourier methods are then employed to handle the linear and quadratic terms. The main theorem is also given in a version that more easily lends itself to applications.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 2 (1977), 357-369.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343800

**Digital Object Identifier**

doi:10.1214/aos/1176343800

**Mathematical Reviews number (MathSciNet)**

MR518648

**Zentralblatt MATH identifier**

0356.62015

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 62G30: Order statistics; empirical distribution functions

**Keywords**

Error bounds linear combinations of order statistics elementary methods Fourier methods

#### Citation

Bjerve, Steinar. Error Bounds for Linear Combinations of Order Statistics. Ann. Statist. 5 (1977), no. 2, 357--369. doi:10.1214/aos/1176343800. https://projecteuclid.org/euclid.aos/1176343800