Asymptotically efficient sequential kernel estimates of the drift coefficient in ergodic diffusion processes

DOI10.1007/s11203-005-3248-4zbMath1117.62083OpenAlexW1973164921MaRDI QIDQ995842

Leonid I. Galtchouk, Serguei Pergamenchtchikov

Publication date: 10 September 2007

Published in: Statistical Inference for Stochastic Processes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11203-005-3248-4

zbMATH Keywords

minimaxergodic diffusion processdriftnonparametric sequential estimationefficient procedure

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05) Sequential estimation (62L12)

Related Items (9)

ADAPTIVE ESTIMATION IN A HETEROSCEDASTIC NONPARAMETRIC REGRESSION ⋮ Adaptive efficient analysis for big data ergodic diffusion models ⋮ Uniform concentration inequality for ergodic diffusion processes ⋮ Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions ⋮ Sequential robust estimation for nonparametric autoregressive models ⋮ Adaptive sequential estimation for ergodic diffusion processes in quadratic metric ⋮ Asymptotically efficient estimates for nonparametric regression models ⋮ Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models ⋮ Sequential model selection method for nonparametric autoregression

Cites Work

• Spline smoothing in regression models and asymptotic efficiency in \(L_ 2\)
• Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
• Optimal global rates of convergence for nonparametric regression
• Adaptive drift estimation for nonparametric diffusion model.
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Recursive Estimation in Diffusion Model
• Identification of Nonstationary Diffusion Model by the Method of Sieves
• Adaptive Spline Estimates for Nonparametric Regression Models
• Nonparametric Identification for Diffusion Processes
• Local minimax pointwise estimation of a multivariate density
• An Asymptotically Minimax Regression Estimator in the Uniform Norm up to Exact Constant
• Nonparametric Sequential Minimax Estimation of the Drift Coefficient in Diffusion Processes

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