WIAS Preprint No. 504, (1999)

Adaptive drift estimation for nonparametric diffusion model


  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62M99


  • drift and diffusion coefficients, nonparametric estimation, bandwidth selection




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 log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.

Appeared in

  • Ann. Statist., 28(2000), pp. 815-836

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