Robust Semiparametric Graphical Models with Skew-Elliptical Distributions

2025/01/14 by Di Luzio, Gabriele, Morelli, Giacomo
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2501.08033

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.

Related

• High Dimensional Semiparametric Gaussian Copula Graphical Models
• Higher Moment Estimation for Elliptically-distributed Data: Is it Necessary to Use a Sledgehammer to Crack an Egg?
• ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models
• The Elliptical Processes: a Family of Fat-tailed Stochastic Processes
• A new robust class of skew elliptical distributions