Robust Semiparametric Graphical Models with Skew-Elliptical Distributions

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.