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arXiv · 2501.08033

Robust Semiparametric Graphical Models with Skew-Elliptical Distributions

Gabriele Di Luzio·Giacomo Morelli
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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.

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Gabriele Di Luzio, Giacomo Morelli. 2025-01-14. Robust Semiparametric Graphical Models with Skew-Elliptical Distributions. https://arxiv.org/abs/2501.08033

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