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April, 1981 Weak Convergence of the Empirical Characteristic Function
Michael B. Marcus
Ann. Probab. 9(2): 194-201 (April, 1981). DOI: 10.1214/aop/1176994461


Let $X$ be a real valued random variable with probability distribution function $F(x)$ and characteristic function $c(t)$. Let $F_n(x)$ be the $n$th empirical distribution function associated with $X$ and $c_n(t)$ the characteristic function of $F_n(x)$. Necessary and sufficient conditions are obtained for the weak convergence of $\sqrt{n}\lbrack c_n(t) - c(t)\rbrack$ on the space of continuous complex valued functions on $\lbrack -1/2, 1/2\rbrack$.


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Michael B. Marcus. "Weak Convergence of the Empirical Characteristic Function." Ann. Probab. 9 (2) 194 - 201, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0465.60008
MathSciNet: MR606982
Digital Object Identifier: 10.1214/aop/1176994461

Primary: 60B10
Secondary: 60F05

Keywords: central limit theorem on $C(\lbrack - 1/2, 1/2 \rbrack)$ , Empirical characteristic function , empirical distribution theorem , subgaussian processes

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 2 • April, 1981
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