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

Nicolas Marie (1) , Amélie Rosier (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 ESME - ESME - École spéciale de mécanique et d'électricité

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.

Domaines: Statistiques [math.ST]

Nicolas Marie, Amélie Rosier. Nadaraya-Watson Estimator for I.I.D. Paths of Diffusion Processes. Scandinavian Journal of Statistics, 2022, 50 (2), pp.589-637. ⟨10.1111/sjos.12593⟩. ⟨hal-03226531v3⟩