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On the first zero of an empirical characteristic function

Published online by Cambridge University Press:  14 July 2016

H. U. Bräker  and
J. Hüsler
H. U. Bräker
Affiliation:
University of Bern
J. Hüsler*
Affiliation:
University of Bern
*
∗ Postal address: Department of Mathematical Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
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Abstract

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

Keywords

GAUSSIAN PROCESSESSTABLE LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 593 - 601
Copyright
Copyright © Applied Probability Trust 1991 

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