Brouste, Alexandre; Soltane, Marius; Votsi, Irene One-step estimation for the fractional Gaussian noise at high-frequency. (English) Zbl 1454.62092 ESAIM, Probab. Stat. 24, 827-841 (2020). Summary: 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. Cited in 2 Documents MSC: 62F12 Asymptotic properties of parametric estimators 62M09 Non-Markovian processes: estimation Keywords:fractional Gaussian noise; infill asymptotics; efficient estimation; Fisher scoring Software:R PDFBibTeX XMLCite \textit{A. Brouste} et al., ESAIM, Probab. Stat. 24, 827--841 (2020; Zbl 1454.62092) Full Text: DOI References: [1] A. Aït-Sahalia and J. Jacod, Fisher’s information for discretely sampled Lévy processes. Econometrica 76 (2008) 727-761. · Zbl 1144.62070 [2] C. Berzin and J. Léon, Estimation in models driven by fractional Brownian motion. Ann. Inst. Henri Poincaré - Probab. Statist. 44 (2008) 191-213. · Zbl 1206.62141 [3] A. Brouste and M. Fukasawa, Local asymptotic normality property for fractional Gaussian noise under high-frequency observations. Ann. Statist. 46 (2018) 2045-2061. · Zbl 1411.62045 [4] A. Brouste and H. Masuda, Efficient estimation of stable Lévy process with symmetric jumps. Statist. Inference Stoch. 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