Parametric estimation for convolutionally observed diffusion processes

TL;DR

This paper introduces a convolutional observation scheme for diffusion processes, enabling smoother data analysis, and develops estimation and testing methods validated through simulations and real EEG data application.

Contribution

It presents a novel convolutional observation framework and associated estimation and testing theories for diffusion processes, including practical validation.

Findings

Effective estimation of diffusion parameters demonstrated

Smoothing observation improves analysis accuracy

Real EEG data analysis confirms method's applicability

Abstract

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion processes and some kernel functions with respect to time parameter. We discuss the estimation and test theories for the parameter determining the smoothness of the observation, as well as the least-square-type estimation for the parameters in the diffusion coefficient and the drift one of the latent diffusion process. In addition to the theoretical discussion, we also examine the performance of the estimation and the test with computational simulation, and show an example of real data analysis for one EEG data whose observation can be regarded as smoother one than ordinary diffusion processes with statistical significance.