Nadaraya-Watson Type Estimator of the Transition Density Function for Diffusion Processes

TL;DR

This paper introduces a nonparametric Nadaraya-Watson estimator for the transition density of diffusion processes, providing risk bounds, an improved bandwidth selection method, and supporting numerical experiments.

Contribution

It presents a novel NW estimator for diffusion transition densities with theoretical risk bounds and an enhanced bandwidth selection approach.

Findings

Risk bounds established for the estimator

Effective bandwidth selection method proposed

Numerical experiments validate the approach

Abstract

This paper deals with a nonparametric Nadaraya-Watson (NW) estimator of the transition density function computed from independent continuous observations of a diffusion process. A risk bound is established on this estimator. The paper also deals with an extension of the penalized comparison to overfitting bandwidths selection method for our NW estimator. Finally, numerical experiments are provided.