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.
Publié le : 1977-05-14
Classification:
Order statistics,
law of the iterated logarithm,
empirical df,
nearly linear bounds,
quantile process,
60F15,
62G30
@article{1176343845,
author = {Wellner, Jon A.},
title = {A Law of the Iterated Logarithm for Functions of Order Statistics},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 481-494},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343845}
}
Wellner, Jon A. A Law of the Iterated Logarithm for Functions of Order Statistics. Ann. Statist., Tome 5 (1977) no. 1, pp. 481-494. http://gdmltest.u-ga.fr/item/1176343845/