Adaptive drift estimation for nonparametric diffusion model
非参数扩散模型的自适应漂移估计
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.