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

arXiv: https://arxiv.org/abs/1502.07641 · HTML: https://mlsanity.com/paper/1502.07641/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2015.

## Built on by (most cited first, 5 of 5)

- [Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques](https://mlsanity.com/paper/2102.09743/) (2021)
- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note](https://mlsanity.com/paper/2605.27563/) (2026)

## Abstract (arXiv)

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 Xa and Xb 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 Omega (the inverse of the covariance matrix Sigma). 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 Omegaab 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.