continuous-time observation; high frequency data; Parameter estimation; rate of normal convergence of the estimators; stationary Gaussian processes; strong consistency; Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] Let Z:= {Zt, t ≥ 0} be a stationary Gaussian process. We study two estimators of E[Z02], namely ̂fT (Z):=1 ∫T T 0Z2tdt, and ˜fn(Z):= 1 ∑n n i=1Z2ti, where ti = iΔn, i = 0, 1, …, n, Δn → 0 and Tn:= nΔn → ∞. We prove that the two estimators are strongly consistent and estab-lish Berry-Esseen bounds for a central limit theorem involvinĝfT (Z) and ˜fn(Z). We apply these results to asymptotically stationary Gaussian processes and estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes.
Disciplines :
Mathematics
Author, co-author :
Douissi, Soukaina; National School of Applied Sciences, Marrakech, Morocco
Es-Sebaiy, Khalifa; Department of Mathematics, Faculty of Science, Kuwait University, Kuwait
KERCHEV, George ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Mathematics > Team Ivan NOURDIN
NOURDIN, Ivan ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
yes
Language :
English
Title :
Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency
Publication date :
2022
Journal title :
Electronic Journal of Statistics
eISSN :
1935-7524
Publisher :
Institute of Mathematical Statistics
Volume :
16
Issue :
1
Pages :
636 - 670
Peer reviewed :
Peer Reviewed verified by ORBi
Name of the research project :
R-AGR-3585 - O18/12582675 APOGee (01/09/2019 - 31/08/2022) - NOURDIN Ivan
Funders :
FNR - Fonds National de la Recherche
Funding text :
arXiv: 2102.04810 ∗G. Kerchev and I. Nourdin were supported by the FNR grant APOGEe (R-AGR-3585-10) at Luxembourg University.
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