Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory

Mohamedou Ould Haye

ESAIM: Probability and Statistics (2002)

  • Volume: 6, page 293-309
  • ISSN: 1292-8100

Abstract

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We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and U -Statistics.

How to cite

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Haye, Mohamedou Ould. "Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory." ESAIM: Probability and Statistics 6 (2002): 293-309. <http://eudml.org/doc/245390>.

@article{Haye2002,
abstract = {We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and $U$-Statistics.},
author = {Haye, Mohamedou Ould},
journal = {ESAIM: Probability and Statistics},
keywords = {empirical process; Hermite polynomials; Rosenblatt processes; seasonal long-memory; $U$-statistics; von–Mises functionals},
language = {eng},
pages = {293-309},
publisher = {EDP-Sciences},
title = {Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory},
url = {http://eudml.org/doc/245390},
volume = {6},
year = {2002},
}

TY - JOUR
AU - Haye, Mohamedou Ould
TI - Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory
JO - ESAIM: Probability and Statistics
PY - 2002
PB - EDP-Sciences
VL - 6
SP - 293
EP - 309
AB - We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and $U$-Statistics.
LA - eng
KW - empirical process; Hermite polynomials; Rosenblatt processes; seasonal long-memory; $U$-statistics; von–Mises functionals
UR - http://eudml.org/doc/245390
ER -

References

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