ROCKET: Robust Confidence Intervals Via Kendall's Tau for Transelliptical Graphical Models

Undirected graphical models are used extensively in the biological and social sciences to encode a pattern of conditional independences between variables, where the absence of an edge between two nodes a and b indicates that the corresponding two variables X_a and X_b are believed to be conditionally independent, after controlling for all other measured variables. In the Gaussian case, conditional independence corresponds to a zero entry in the precision matrix Ω (the inverse of the covariance matrix Σ). Real data often exhibits heavy tail dependence between variables, which cannot be captured by the commonly used Gaussian or nonparanormal (Gaussian copula) graphical models. Kolar studied the trans elliptical model, an elliptical copula model that generalizes Gaussian and nonparanormal models to a broader family of distributions. He proposed the ROCKET method, which constructs an estimator of Ω_ab that he proved to be asymptotically normal under mild assumptions. Empirically, ROCKET outperforms the nonparanormal and Gaussian models in terms of achieving accurate inference on simulated data. He also compared the three methods on real data (daily stock returns), and found that the ROCKET estimator is the only method whose behavior across subsamples agrees with the distribution predicted by the theory.

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Nonlinear Algebra and Statistics (NLASTATS)