Sure Screening for Transelliptical Graphical Models

TL;DR

This paper introduces a computationally efficient sure screening method for high-dimensional transelliptical graphical models, accurately recovering the true graph structure with controlled false positives.

Contribution

It proposes a novel thresholding approach based on Kendall's tau for estimating the graph structure in transelliptical models, ensuring high probability of true edge inclusion.

Findings

Method performs well in simulations

Competitive with more complex techniques

Controls false positive rate effectively

Abstract

We propose a sure screening approach for recovering the structure of a transelliptical graphical model in the high dimensional setting. We estimate the partial correlation graph by thresholding the elements of an estimator of the sample correlation matrix obtained using Kendall's tau statistic. Under a simple assumption on the relationship between the correlation and partial correlation graphs, we show that with high probability, the estimated edge set contains the true edge set, and the size of the estimated edge set is controlled. We develop a threshold value that allows for control of the expected false positive rate. In simulation and on an equities data set, we show that transelliptical graphical sure screening performs quite competitively with more computationally demanding techniques for graph estimation.