ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models
This provides a robust statistical tool for researchers in fields like biology and finance dealing with non-Gaussian data, though it is an incremental extension of existing models.
The paper tackles the problem of modeling conditional independence in heavy-tailed data by proposing the ROCKET method for transelliptical graphical models, which outperforms Gaussian and nonparanormal models in simulations and shows consistent behavior on real stock return data.
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. In this paper, we study the transelliptical model, an elliptical copula model that generalizes Gaussian and nonparanormal models to a broader family of distributions. We propose the ROCKET method, which constructs an estimator of $Ω_{ab}$ that we prove to be asymptotically normal under mild assumptions. Empirically, ROCKET outperforms the nonparanormal and Gaussian models in terms of achieving accurate inference on simulated data. We also compare the three methods on real data (daily stock returns), and find that the ROCKET estimator is the only method whose behavior across subsamples agrees with the distribution predicted by the theory.