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November, 1976 A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution
H. Hecker
Ann. Statist. 4(6): 1244-1246 (November, 1976). DOI: 10.1214/aos/1176343656

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.

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H. Hecker. "A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution." Ann. Statist. 4 (6) 1244 - 1246, November, 1976. https://doi.org/10.1214/aos/1176343656

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0345.62033
MathSciNet: MR423642
Digital Object Identifier: 10.1214/aos/1176343656

Subjects:
Primary: 62G30
Secondary: 60F05 , 62E20

Keywords: asymptotic normality , linear combinations of order statistics

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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