The Annals of Statistics

A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution

H. Hecker

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Abstract

A necessary and sufficient condition for the asymptotic normality of linear combinations of order statistics from the uniform distribution over [0, 1] is derived. The condition implies, that the variances of all weighted extremes are asymptotically zero compared with the total variance of the sum, which conversely, in the case of nonnegative constants, is sufficient for the asymptotic normality.

Article information

Source
Ann. Statist., Volume 4, Number 6 (1976), 1244-1246.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343656

Digital Object Identifier
doi:10.1214/aos/1176343656

Mathematical Reviews number (MathSciNet)
MR423642

Zentralblatt MATH identifier
0345.62033

JSTOR
links.jstor.org

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems

Keywords
Linear combinations of order statistics asymptotic normality

Citation

Hecker, H. A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution. Ann. Statist. 4 (1976), no. 6, 1244--1246. doi:10.1214/aos/1176343656. https://projecteuclid.org/euclid.aos/1176343656


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