The present paper concerns the parametric estimation for the fractional Gaussian noise in a high-frequency observation scheme. The sequence of Le Cam’s one-step maximum likelihood estimators (OSMLE) is studied. This sequence is defined by an initial sequence of quadratic generalized variations-based estimators (QGV) and a single Fisher scoring step. The sequence of OSMLE is proved to be asymptotically efficient as the sequence of maximum likelihood estimators but is much less computationally demanding. It is also advantageous with respect to the QGV which is not variance efficient. Performances of the estimators on finite size observation samples are illustrated by means of Monte-Carlo simulations.
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DOI : 10.1051/ps/2020022
Mots-clés : Fractional Gaussian noise, infill asymptotics, efficient estimation, Fisher scoring
@article{PS_2020__24_1_827_0,
author = {Brouste, Alexandre and Soltane, Marius and Votsi, Irene},
title = {One-step estimation for the fractional {Gaussian} noise at high-frequency},
journal = {ESAIM: Probability and Statistics},
pages = {827--841},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2020022},
mrnumber = {4178369},
zbl = {1454.62092},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2020022/}
}
TY - JOUR AU - Brouste, Alexandre AU - Soltane, Marius AU - Votsi, Irene TI - One-step estimation for the fractional Gaussian noise at high-frequency JO - ESAIM: Probability and Statistics PY - 2020 SP - 827 EP - 841 VL - 24 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2020022/ DO - 10.1051/ps/2020022 LA - en ID - PS_2020__24_1_827_0 ER -
%0 Journal Article %A Brouste, Alexandre %A Soltane, Marius %A Votsi, Irene %T One-step estimation for the fractional Gaussian noise at high-frequency %J ESAIM: Probability and Statistics %D 2020 %P 827-841 %V 24 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2020022/ %R 10.1051/ps/2020022 %G en %F PS_2020__24_1_827_0
Brouste, Alexandre; Soltane, Marius; Votsi, Irene. One-step estimation for the fractional Gaussian noise at high-frequency. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 827-841. doi : 10.1051/ps/2020022. http://www.numdam.org/articles/10.1051/ps/2020022/
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