The Annals of Statistics
- Ann. Statist.
- Volume 5, Number 3 (1977), 481-494.
A Law of the Iterated Logarithm for Functions of Order Statistics
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.
Ann. Statist., Volume 5, Number 3 (1977), 481-494.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F15: Strong theorems
Secondary: 62G30: Order statistics; empirical distribution functions
Wellner, Jon A. A Law of the Iterated Logarithm for Functions of Order Statistics. Ann. Statist. 5 (1977), no. 3, 481--494. doi:10.1214/aos/1176343845. https://projecteuclid.org/euclid.aos/1176343845