Optimal rates for parameter estimation of stationary Gaussian processes

DOI10.1016/j.spa.2018.08.010zbMath1422.60031arXiv1603.04542OpenAlexW2963296412WikidataQ129208799 ScholiaQ129208799MaRDI QIDQ2274291

Khalifa Es-Sebaiy, Frederi G. Viens

Publication date: 19 September 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.04542

zbMATH Keywords

parameter estimationfractional Brownian motioncentral limit theoremstationary Gaussian processesBerry-Esséen theoremNourdin-Peccati analysis

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Non-Markovian processes: estimation (62M09)

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Uses Software

• DLMF
• YUIMA

Cites Work

• Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind
• Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes
• Quantitative Breuer-Major theorems
• Parameter estimation for fractional Ornstein-Uhlenbeck processes
• Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
• Fractional {O}rnstein-{U}hlenbeck processes
• Statistical analysis of the fractional Ornstein--Uhlenbeck type process
• Functional quantization of Gaussian processes
• Convergence in total variation on Wiener chaos
• Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package
• The total variation distance between two double Wiener-Itô integrals
• A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise
• Central limit theorems for sequences of multiple stochastic integrals
• Statistical aspects of the fractional stochastic calculus
• Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes
• On fractional Ornstein-Uhlenbeck processes
• A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences
• Parameter Estimation for Fractional Ornstein–Uhlenbeck Processes with Discrete Observations
• Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants
• Normal Approximations with Malliavin Calculus
• Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise
• The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations
• The Malliavin Calculus and Related Topics
• Non-central limit theorems for non-linear functional of Gaussian fields
• Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy–Landau–Littlewood inequality
• The optimal fourth moment theorem

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