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 -Statistics.
Keywords: empirical process, Hermite polynomials, Rosenblatt processes, seasonal long-memory, $U$-statistics, von-Mises functionals
@article{PS_2002__6__293_0,
author = {Haye, Mohamedou Ould},
title = {Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory},
journal = {ESAIM: Probability and Statistics},
pages = {293--309},
year = {2002},
publisher = {EDP Sciences},
volume = {6},
doi = {10.1051/ps:2002016},
mrnumber = {1943152},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps:2002016/}
}
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 SP - 293 EP - 309 VL - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps:2002016/ DO - 10.1051/ps:2002016 LA - en ID - PS_2002__6__293_0 ER -
%0 Journal Article %A Haye, Mohamedou Ould %T Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory %J ESAIM: Probability and Statistics %D 2002 %P 293-309 %V 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps:2002016/ %R 10.1051/ps:2002016 %G en %F PS_2002__6__293_0
Haye, Mohamedou Ould. Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 293-309. doi: 10.1051/ps:2002016
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