Tensor Elliptical Graphic Model

TL;DR

This paper introduces a robust method for estimating high-dimensional tensor elliptical graphical models using spatial-sign-based estimators, extending applicability to heavy-tailed distributions beyond the normal case.

Contribution

It develops a novel spatial-sign-based estimator for tensor elliptical graphical models, achieving optimal rates under broader elliptical distributions.

Findings

Estimator performs well under heavy-tailed distributions.

Simulation results confirm robustness and accuracy.

Real data applications demonstrate practical utility.

Abstract

We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed scenarios, motivated by the fact that up to a constant, the spatial-sign covariance matrix can approximate the true covariance matrix when the dimension turns to infinity under tensor elliptical distribution, we proposed a spatial-sign-based estimator to robustly estimate tensor elliptical graphical model, the rate of which matches the existing rate under normality for a wider family of distribution, i.e. elliptical distribution. We also conducted extensive simulations and real data applications to illustrate the practical utility of the proposed methods, especially under heavy-tailed distribution.