Geodesic
Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 293-309

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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.

DOI : 10.1051/ps:2002016
Classification : 60G15, 60G18, 62G30, 62M10
Keywords: empirical process, Hermite polynomials, Rosenblatt processes, seasonal long-memory, $U$-statistics, von-Mises functionals 
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     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},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2002},
     doi = {10.1051/ps:2002016},
     mrnumber = {1943152},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2002016/}
}
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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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