ROCKET
swMATH ID:  30016 
Software Authors:  Barber, Rina Foygel; Kolar, Mladen 
Description:  ROCKET: robust confidence intervals via Kendall’s tau for transelliptical graphical models. Understanding complex relationships between random variables is of fundamental importance in highdimensional statistics, with numerous applications in biological and social sciences. Undirected graphical models are often used to represent dependencies between random variables, where an edge between two random variables is drawn if they are conditionally dependent given all the other measured variables. A large body of literature exists on methods that estimate the structure of an undirected graphical model, however, little is known about the distributional properties of the estimators beyond the Gaussian setting. In this paper, we focus on inference for edge parameters in a highdimensional transelliptical model, which generalizes Gaussian and nonparanormal graphical models. We propose ROCKET, a novel procedure for estimating parameters in the latent inverse covariance matrix. We establish asymptotic normality of ROCKET in an ultra highdimensional setting under mild assumptions, without relying on oracle model selection results. ROCKET requires the same number of samples that are known to be necessary for obtaining a (sqrt{n}) consistent estimator of an element in the precision matrix under a Gaussian model. Hence, it is an optimal estimator under a much larger family of distributions. The result hinges on a tight control of the sparse spectral norm of the nonparametric Kendall’s tau estimator of the correlation matrix, which is of independent interest. 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. 
Homepage:  https://projecteuclid.org/euclid.aos/1536631279 
Keywords:  graphical model selection; transelliptical graphical models; covariance selection; uniformly valid inference; postmodel selection inference; rankbased estimation 
Related Software:  glasso; covTest; TETRAD; huge; Knorm; limma; AdaPT; dSTEM; adaptMT; GEOquery; Bioconductor; MIM; hglasso 
Cited in:  13 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

ROCKET: robust confidence intervals via Kendall’s tau for transelliptical graphical models. Zbl 1410.62059 Barber, Rina Foygel; Kolar, Mladen 
2018

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Cited by 27 Authors
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Cited in 6 Serials
Cited in 2 Fields
13  Statistics (62XX) 
1  Computer science (68XX) 