## The Annals of Statistics

- Ann. Statist.
- Volume 7, Number 5 (1979), 955-959.

### A Differential for $L$-Statistics

#### Abstract

The functional $T(F) = \int F^{-1}(t)J(t) dt$ associated with linear combinations of order statistics is shown to have a Frechet-type differential. As a corollary, the statistic $T(F_n)$ obtained by evaluating $T(\cdot)$ at the sample df $F_n$ is seen to be asymptotically normal and to obey a law of the iterated logarithm.

#### Article information

**Source**

Ann. Statist., Volume 7, Number 5 (1979), 955-959.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344781

**Digital Object Identifier**

doi:10.1214/aos/1176344781

**Mathematical Reviews number (MathSciNet)**

MR536500

**Zentralblatt MATH identifier**

0423.62021

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 62G30: Order statistics; empirical distribution functions

**Keywords**

Differential linear combinations of order statistics asymptotic normality law of the iterated logarithm

#### Citation

Boos, Dennis D. A Differential for $L$-Statistics. Ann. Statist. 7 (1979), no. 5, 955--959. doi:10.1214/aos/1176344781. https://projecteuclid.org/euclid.aos/1176344781