The Annals of Statistics

A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics

Jon A. Wellner

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Abstract

A strengthened version of the Glivenko-Cantelli theorem for the uniform empirical distribution function is proved. The strengthened Glivenko-Cantelli theorem is used to establish strong laws of large numbers for linear functions of order statistics.

Article information

Source
Ann. Statist., Volume 5, Number 3 (1977), 473-480.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343844

Digital Object Identifier
doi:10.1214/aos/1176343844

Mathematical Reviews number (MathSciNet)
MR651528

Zentralblatt MATH identifier
0365.62045

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Glivenko-Cantelli theorem order statistics strong laws of large numbers

Citation

Wellner, Jon A. A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics. Ann. Statist. 5 (1977), no. 3, 473--480. doi:10.1214/aos/1176343844. https://projecteuclid.org/euclid.aos/1176343844


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Corrections

  • See Correction: Jon A. Wellner. Correction to: A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics. Ann. Statist., Volume 6, Number 6 (1978), 1394--1394.