Robust Semiparametric Graphical Models with Skew-Elliptical Distributions

TL;DR

This paper introduces elliptical skew-(S)KEPTIC, a semiparametric estimator for robustly estimating non-Gaussian graphical models with skewness, demonstrating improved graph recovery and application to stock return data.

Contribution

It extends the elliptical framework to skew-elliptical distributions, providing robust convergence guarantees and practical advantages over Gaussian models.

Findings

Achieves robust convergence rates for graph recovery and parameter estimation.

Demonstrates reliable graph recovery in simulations.

Produces sparser, more realistic graphs for stock returns.

Abstract

We propose semiparametric estimators, called elliptical skew-(S)KEPTIC, for efficiently and robustly estimating non-Gaussian graphical models. Our approach extends the semiparametric elliptical framework to the meta skew-elliptical family, which accommodates skewness. Theoretically, we show that the elliptical skew-(S)KEPTIC estimators achieve robust convergence rates for both graph recovery and parameter estimation. Through numerical simulations, we illustrate the reliable graph recovery performance of the elliptical skew-(S)KEPTIC estimators. Finally, we apply the new method to the daily log-returns of the stocks in the S\&P 500 index and obtain a sparser graph than with Gaussian copula graphical models.