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 high-dimensional 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 high-dimensional 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 high-dimensional 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; post-model selection inference; rank-based 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 1410.62059Barber, Rina Foygel; Kolar, Mladen 2018 all top 5 Cited by 29 Authors 4 Kolar, Mladen 2 Foygel Barber, Rina 2 Liu, Han 2 Ning, Yang 2 Ren, Zhao 1 Bunea, Florentina 1 Cai, Tony Tony 1 Dai, Ran 1 Dinicu, Claudiu 1 Eisenach, Carson 1 Fujisawa, Hironori 1 He, Yong 1 Hirose, Kei-ichi 1 Ji, Jiadong 1 Li, Ang 1 Liu, Jun S. 1 Liu, Xiumin 1 Liu, Yu 1 Lu, Junwei 1 Neykov, Matey 1 Niu, Lu 1 Rossell, David 1 Sese, Jun 1 Yu, Ming 1 Zhang, Liang 1 Zhang, Xinsheng 1 Zhao, Junlong 1 Zhou, Harrison H. 1 Zwiernik, Piotr all top 5 Cited in 6 Serials 3 Journal of Multivariate Analysis 3 Journal of Machine Learning Research (JMLR) 3 Electronic Journal of Statistics 2 The Annals of Statistics 1 Statistical Science 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology Cited in 2 Fields 13 Statistics (62-XX) 1 Computer science (68-XX) Citations by Year