Volume 24, 2020
|Page(s)||827 - 841|
|Published online||24 November 2020|
One-step estimation for the fractional Gaussian noise at high-frequency
Laboratoire Manceau de Mathématiques, Le Mans Université,
Le Mans, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 17 September 2020
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.
Mathematics Subject Classification: 62F12 / 62M09 / 65U05
Key words: Fractional Gaussian noise / infill asymptotics / efficient estimation / Fisher scoring
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.