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

Abstract

This paper deals with a nonparametric Nadaraya-Watson estimator $\hat{b}$ of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on $\hat{b}$ 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 $\hat{b}$. Finally, some numerical experiments are provided.

arXiv comment40 pages, 6 figures

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• Nonparametric Drift Estimation from Diffusions with Correlated Brownian Motions
• On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE
• Nonparametric Estimation of the Transition Density Function for Diffusion Processes
• On a Projection Least Squares Estimator for Jump Diffusion Processes