Nadaraya-Watson Estimator for I.I.D. Paths of Diffusion Processes

This paper deals with a nonparametric Nadaraya-Watson estimator $\widehat b$ of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on $\widehat b$ and its discrete-time approximation are established. The paper also deals with extensions of the PCO and leave-one-out cross validation bandwidth selection methods for $\widehat b$. Finally, some numerical experiments are provided.