Gaussian stationary processes over graphs, general frame and maximum likelihood identification

TL;DR

This paper extends spectral theory to Gaussian ARMA processes on graphs, developing maximum likelihood estimation methods and demonstrating their asymptotic optimality for parameter identification.

Contribution

It introduces a spectral framework for Gaussian processes on graphs and extends Whittle maximum likelihood estimation to this setting, proving asymptotic optimality.

Findings

Extended Whittle likelihood to graph-indexed Gaussian processes

Proved asymptotic optimality of the proposed estimation method

Provided a spectral theory framework for processes over graphs

Abstract

In this paper, using spectral theory of Hilbertian operators, we study ARMA Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their asymptotic optimality.