A Law of the Iterated Logarithm for Functions of Order Statistics
The Annals of Statistics · 1977 · Volume 5 · Issue 3
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.
Keywords
60F15, 62G30, empirical df, Law of the iterated logarithm, nearly linear bounds, order statistics, quantile process
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