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.
Citation
Jon A. Wellner. "A Law of the Iterated Logarithm for Functions of Order Statistics." Ann. Statist. 5 (3) 481 - 494, May, 1977. https://doi.org/10.1214/aos/1176343845
Information
