Nadaraya–Watson estimator for I.I.D. paths of diffusion processes

Abstract

Abstract This paper deals with a nonparametric Nadaraya–Watson (NW) estimator of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on the estimator 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 our NW estimator. Finally, some numerical experiments are provided.