## The Annals of Statistics

### A Law of the Iterated Logarithm for Functions of Order Statistics

Jon A. Wellner

#### Abstract

A general law of the iterated logarithm for linear combinations of order statistics is proved. The key tools are (1) iterated logarithm convergence of the uniform empirical process $U_n$ in $\rho_q$-metrics due to B. R. James and (2) almost sure "nearly linear" bounds for the empirical distribution function. A law of the iterated logarithm for the quantile process is also established.

#### Article information

Source
Ann. Statist., Volume 5, Number 3 (1977), 481-494.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343845

Digital Object Identifier
doi:10.1214/aos/1176343845

Mathematical Reviews number (MathSciNet)
MR436297

Zentralblatt MATH identifier
0365.62046

JSTOR