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January, 1989 Laws of the Iterated Logarithm for the Empirical Characteristic Function
Michael T. Lacey
Ann. Probab. 17(1): 292-300 (January, 1989). DOI: 10.1214/aop/1176991509


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 $\lbrack -1, 1 \rbrack$.


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Michael T. Lacey. "Laws of the Iterated Logarithm for the Empirical Characteristic Function." Ann. Probab. 17 (1) 292 - 300, January, 1989.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0671.60005
MathSciNet: MR972786
Digital Object Identifier: 10.1214/aop/1176991509

Primary: 60B12
Secondary: 60G10 , 60G50

Keywords: Empirical characteristic function , Laws of the iterated logarithm , Metric entropy , Stationary Gaussian processes

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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