Adaptive Drift Estimation for Nonparametric Diffusion Model

We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and n...

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Bibliographic Details
Published in:The Annals of statistics 2000-06, Vol.28 (3), p.815-836
Main Author: Spokoiny, Vladimir G.
Format: Article
Language:English
Subjects:
62G05
62M99
bandwidth selection
Coefficients
Diffusion coefficient
Drift and diffusion coefficients
Ergodic theory
Estimate reliability
Estimators
Exact sciences and technology
Inference for Stochastic Processes
Inference from stochastic processes
time series analysis
Martingales
Mathematical functions
Mathematics
nonparametric estimation
Nonparametric inference
Nonparametric models
Parametric inference
Point estimators
Probability and statistics
Sciences and techniques of general use
Statistics
Stochastic processes
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Description
Summary:We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1015951999