Adaptive drift estimation for nonparametric diffusion model
- Spokoiny, Vladimir
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.
- Ann. Statist., 28(2000), pp. 815-836