## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 43, Number 2 (1972), 412-427.

### Functions of Order Statistics

#### Abstract

Two theorems on the asymptotic normality of linear combinations of functions of order statistics are given. Theorem 1 requires a "smooth" scoring function but the underlying df need not be continuous even and can also depend on the sample size. Theorem 2 allows general scoring functions but places additional restrictions on the df. Applications included.

#### Article information

**Source**

Ann. Math. Statist., Volume 43, Number 2 (1972), 412-427.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177692622

**Digital Object Identifier**

doi:10.1214/aoms/1177692622

**Mathematical Reviews number (MathSciNet)**

MR301846

**Zentralblatt MATH identifier**

0239.62037

**JSTOR**

links.jstor.org

#### Citation

Shorack, Galen R. Functions of Order Statistics. Ann. Math. Statist. 43 (1972), no. 2, 412--427. doi:10.1214/aoms/1177692622. https://projecteuclid.org/euclid.aoms/1177692622