## The Annals of Statistics

### A Differential for $L$-Statistics

Dennis D. Boos

#### 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

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
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