Let $X$ be a real-valued random variable with distribution function $F(x)$ and characteristic function $c(t)$. Let $F_n(x)$ be the $n$th empirical distribution function associated with $X$ and let $c_n(t)$ be the characteristic function $F_n(x)$. Necessary and sufficient conditions in terms of $c(t)$ are obtained for $c_n(t) - c(t)$ to obey bounded and compact laws of the iterated logarithm in the Banach space of continuous complex-valued functions on $\lbrack -1, 1 \rbrack$.
Publié le : 1989-01-14
Classification:
Laws of the iterated logarithm,
empirical characteristic function,
stationary Gaussian processes,
metric entropy,
60B12,
60G50,
60G10
@article{1176991509,
author = {Lacey, Michael T.},
title = {Laws of the Iterated Logarithm for the Empirical Characteristic Function},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 292-300},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991509}
}
Lacey, Michael T. Laws of the Iterated Logarithm for the Empirical Characteristic Function. Ann. Probab., Tome 17 (1989) no. 4, pp. 292-300. http://gdmltest.u-ga.fr/item/1176991509/