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rosenblatt processes

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Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonallong-memory
Mohamedou Ould Haye
Journal:

ESAIM: Probability and Statistics / Volume 6 / 2002

Published online by Cambridge University Press:

15 November 2002, pp. 293-309

Print publication:

2002
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We study the asymptotic behavior of the empirical process when theunderlying data are Gaussian and exhibit seasonallong-memory. We prove that the limiting process can be quitedifferent from the limit obtained in the case of regularlong-memory. However, in both cases, the limiting process isdegenerated. We apply our results to von–Mises functionals andU-Statistics.