## The Annals of Statistics

### Asymptotic Normality of Linear Combinations of Order Statistics with a Smooth Score Function

David M. Mason

#### Abstract

Asymptotic normality of linear combinations of order statistics of the form $T_n = n^{-1} \sum J(i/(n + 1))X_{in}$ is investigated along with a slightly trimmed version of $T_n$. Theorem 5 of Stigler (1974) is extended to show asymptotic normality of $T_n$ for a wide class of score functions. In addition, a proof of Theorem 4 of Stigler (1974) is given.

#### Article information

Source
Ann. Statist., Volume 9, Number 4 (1981), 899-908.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345531

Digital Object Identifier
doi:10.1214/aos/1176345531

Mathematical Reviews number (MathSciNet)
MR619294

Zentralblatt MATH identifier
0472.62057

JSTOR