Penalized nonparametric mean square estimation of the coefficients of diffusion processes

DOI10.3150/07-BEJ5173zbMath1127.62067arXiv0708.4165MaRDI QIDQ2465276

Yves Rozenholc, Valentine Genon-Catalot, Fabienne Comte

Publication date: 9 January 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.4165

zbMATH Keywords

drift and diffusion coefficientsadaptive estimationdiscrete time observationspenalized contrastretrospective simulationmean square estimator model selection

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05)

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Cites Work

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• Sharp adaptive estimation of the drift function for ergodic diffusions
• Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
• Estimating equations based on eigenfunctions for a discretely observed diffusion process
• Risk bounds for model selection via penalization
• Inequalities for absolutely regular sequences: application to density estimation
• Statistical inference for ergodic diffusion processes.
• Adaptive estimation in diffusion processes.
• Adaptive estimation of mean and volatility functions in (auto-)regressive models.
• Nonparametric estimation of scalar diffusions based on low frequency data
• A new algorithm for fixed design regression and denoising
• Density estimation by wavelet thresholding
• Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local times
• Adaptive drift estimation for nonparametric diffusion model.
• Adaptive estimation in autoregression or \(\beta\)-mixing regression via model selection
• On the Poisson equation and diffusion approximation. I
• Martingale estimation functions for discretely observed diffusion processes
• Exact simulation of diffusions
• Retrospective exact simulation of diffusion sample paths with applications
• Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
• Model selection for regression on a random design
• Ten Lectures on Wavelets
• Nonparametric Identification for Diffusion Processes
• On estimating the diffusion coefficient from discrete observations
• Model selection for (auto-)regression with dependent data
• Non‐parametric Kernel Estimation of the Coefficient of a Diffusion
• Adaptive estimation of the spectrum of a stationary Gaussian sequence