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

摘要

Undirected graphical models are used extensively in the biological and socialsciences to encode a pattern of conditional independences between variables,where the absence of an edge between two nodes $a$ and $b$ indicates that thecorresponding two variables $X_a$ and $X_b$ are believed to be conditionallyindependent, after controlling for all other measured variables. In theGaussian case, conditional independence corresponds to a zero entry in theprecision matrix $\Omega$ (the inverse of the covariance matrix $\Sigma$). Realdata often exhibits heavy tail dependence between variables, which cannot becaptured by the commonly-used Gaussian or nonparanormal (Gaussian copula)graphical models. In this paper, we study the transelliptical model, anelliptical copula model that generalizes Gaussian and nonparanormal models to abroader family of distributions. We propose the ROCKET method, which constructsan estimator of $\Omega_{ab}$ that we prove to be asymptotically normal undermild assumptions. Empirically, ROCKET outperforms the nonparanormal andGaussian models in terms of achieving accurate inference on simulated data. Wealso compare the three methods on real data (daily stock returns), and findthat the ROCKET estimator is the only method whose behavior across subsamplesagrees with the distribution predicted by the theory.