The Annals of Statistics

Error Bounds for Linear Combinations of Order Statistics

Steinar Bjerve

Full-text: Open access

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


Export citation