## The Annals of Statistics

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

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

#### 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

#### 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.Project Euclid: euclid.aos/1176344384