Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments

DOI10.1214/14-AOS1216zbMath1296.62018arXiv1406.5863OpenAlexW3098778929MaRDI QIDQ2510830

Valentine Genon-Catalot, Catherine Larédo

Publication date: 4 August 2014

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5863

zbMATH Keywords

diffusion processdiscrete observationsEuler schemedeficiency distancenonparametric experimentsLe Cam equivalence

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Theory of statistical experiments (62B15) Inference from stochastic processes (62M99) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case ⋮ Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise ⋮ Le cam theory on the comparison of statistical models ⋮ Strong Gaussian approximation of the mixture Rasch model ⋮ Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations ⋮ Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise ⋮ The deficiency introduced by resampling ⋮ Asymptotic Inference for Jump Diffusions with State-Dependent Intensity ⋮ Parametric inference for small variance and long time horizon McKean-Vlasov diffusion models

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic equivalence of nonparametric autoregression and nonparametric regression
• Asymptotic equivalence for inference on the volatility from noisy observations
• Asymptotic equivalence of functional linear regression and a white noise inverse problem
• Asymptotic statistical equivalence for scalar ergodic diffusions
• Asymptotic equivalence of spectral density estimation and Gaussian white noise
• A continuous Gaussian approximation to a nonparametric regression in two dimensions
• Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case
• Asymptotic equivalence for nonparametric regression with multivariate and random design
• Diffusion approximation for nonparametric autoregression
• Asymptotic equivalence of nonparametric regression and white noise
• Asymptotic equivalence of density estimation and Gaussian white noise
• Asymptotic equivalence for nonparametric generalized linear models
• Statistical inference for ergodic diffusion processes.
• Asymptotics in statistics. Some basic concepts.
• Adaptive estimation in diffusion processes.
• Asymptotic equivalence for a null recurrent diffusion
• Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
• Asymptotic nonequivalence of nonparametric experiments when the smoothness index is \(1/2\)
• Asymptotic equivalence theory for nonparametric regression with random design
• Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift
• Asymptotic nonequivalence of GARCH models and diffusions
• Asymptotic equivalence for nonparametric regression
• Asymptotic equivalence for nonparametric regression with non-regular errors
• A sufficient condition for asymptotic sufficiency of incomplete observations of a diffusion process
• Asymptotic approximation of nonparametric regression experiments with unknown variances
• Penalized nonparametric mean square estimation of the coefficients of diffusion processes
• Estimation of an Ergodic Diffusion from Discrete Observations
• Diffusions with measurement errors. I. Local Asymptotic Normality
• Maximnm contrast estimation for diffusion processes from discrete observations
• Introduction to nonparametric estimation