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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1051/ps/2020022/
[1] and , Fisher’s information for discretely sampled Lévy processes. Econometrica 76 (2008) 727–761. | DOI | MR | Zbl
[2] and , Estimation in models driven by fractional Brownian motion. Ann. Inst. Henri Poincaré - Probab. Statist. 44 (2008) 191–213. | DOI | Numdam | MR | Zbl
[3] and , Local asymptotic normality property for fractional Gaussian noise under high-frequency observations. Ann. Statist. 46 (2018) 2045–2061. | DOI | MR | Zbl
[4] and , Efficient estimation of stable Lévy process with symmetric jumps. Statist. Inference Stoch. Processes 21 (2018) 289–307. | DOI | MR | Zbl
[5] , Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. J. Statist. Softw. 5 (2000) 1–53. | DOI
[6] , , and , LAN property for some fractional type Brownian motion. ALEA: Latin Am. J. Probab. Math. Statist. 10 (2013) 91–106. | MR | Zbl
[7] , Efficient parameter estimation for self-similar processes. Ann. Statist. 17 (1989) 1749–1766. | DOI | MR | Zbl
[8] , Correction efficient parameter estimation for self-similar processes. Ann. Statist. 34 (2006) 1045–1047. | DOI | MR
[9] , Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. Inform. Theory 38 (1992) 910–917. | DOI | MR | Zbl
[10] and , Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 (1986) 517–532. | MR | Zbl
[11] and , Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations. Bernoulli 25 (2019) 1870–1900. | DOI | MR | Zbl
[12] and , Convergence en loi des H-variations d’un processus gaussien stationnaire sur R. Ann. Inst. Henri Poincaré - Probab. Statist. B 25 (1989) 265–282. | Numdam | MR | Zbl
[13] , Local asymptotic minimax and admissibility in estimation, in Proceedings of 6th Berkeley Symposium on Math. Statist. Prob. (1972) 175–194. | MR | Zbl
[14] and , Statistical Estimation: Asymptotic Theory. Springer-Verlag (1981). | DOI | Zbl
[15] and , Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Instit. Henri Poincaré - Probab. Statist. B 33 (1997) 407–436. | DOI | Numdam | MR | Zbl
[16] , Fisher information for fractional Brownian motion under high-frequency discrete sampling. Commun. Statist. - Theory Methods 42 (2013) 1628–1636. | DOI | MR | Zbl
[17] and , On multi-step MLE-process for Markov sequences. Metrika 79 (2016) 705–724. | DOI | MR | Zbl
[18] , Limits of experiments, in Proceedings of the 6th Berkeley Symposium (1972) 245–261. | MR | Zbl
[19] , On the asymptotic theory of estimation and testing hypothesis, in Proceedings of the 3rd Berkeley Symposium (1956) 355–368. | MR | Zbl
[20] , and , Estimation of the linear fractional stable motion. Bernoulli 26 (2020) 226–252. | DOI | MR | Zbl
[21] R Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing Vienna, Austria. Available from: https://www.R-project.org/ (2016).
[22] and , Stable Non-Gaussian Random Processes. Chapman & Hall (2000). | MR | Zbl
[23] , Uniform asymptotic normality of the maximum likelihood estimator. Ann. Statist. 8 (1980) 1375–1381. | DOI | MR | Zbl
[24] , Asymptotic Statistics. Cambridge University Press (1998). | DOI | MR | Zbl
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