SPECTRODE swMATH ID: 13984 Software Authors: Dobriban, Edgar Description: Efficient computation of limit spectra of sample covariance matrices. Models from random matrix theory (RMT) are increasingly used to gain insights into the behavior of statistical methods under high-dimensional asymptotics. However, the applicability of the framework is limited by numerical problems. Consider the usual model of multivariate statistics where the data is a sample from a multivariate distribution with a given covariance matrix. Under high-dimensional asymptotics, there is a deterministic map from the distribution of eigenvalues of the population covariance matrix (the population spectral distribution or PSD), to the of empirical spectral distribution (ESD). The current methods for computing this map are inefficient, and this limits the applicability of the theory. We propose a new method to compute numerically the ESD from an arbitrary input PSD. Our method, called SPECTRODE, finds the support and the density of the ESD to high precision; we prove this for finite discrete distributions. In computational experiments SPECTRODE outperforms existing methods by orders of magnitude in speed and accuracy. We apply it to compute expectations and contour integrals of the ESD, which are often central in applications.We also illustrate that SPECTRODE is directly useful in statistical problems, such as estimation and hypothesis testing for covariance matrices. Our proposal, implemented in open source software, may broaden the use of RMT in high-dimensional data analysis. Homepage: http://www.worldscientific.com/doi/10.1142/S2010326315500197 Keywords: limiting spectral distribution; sample covariance matrix; Stieltjes transform; high-dimensional statistics; random matrix; multivariate statistics; eigenvalue; empirical spectral distribution; data analysis Related Software: OptShrink; QuEST; RMTool; GCTA; BRENT; leapp; Condor; ePCA; Pyglrm; LowRankModels; DEseq; BayesDA; robustbase Cited in: 12 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Efficient computation of limit spectra of sample covariance matrices. Zbl 1330.65029Dobriban, Edgar 2014 all top 5 Cited by 20 Authors 4 Dobriban, Edgar 2 Heiny, Johannes 2 Leeb, William E. 2 Mikosch, Thomas 2 Singer, Amit 1 Bai, Zhi-Dong 1 Bouchaud, Jean-Philippe 1 Bun, Joël 1 Cordero-Grande, Lucilio 1 Fan, Zhou 1 Johnstone, Iain Murray 1 Ledoit, Olivier 1 Liu, Lydia T. 1 Owen, Art B. 1 Potters, Marc 1 Wolf, Michael 1 Yao, Jianfeng 1 Zheng, Shurong 1 Zhu, Hongtu 1 Zou, Tingting all top 5 Cited in 9 Serials 2 The Annals of Statistics 2 Stochastic Processes and their Applications 2 Computational Statistics and Data Analysis 1 Physics Reports 1 Statistical Papers 1 Advances in Computational Mathematics 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 The Annals of Applied Statistics 1 Random Matrices: Theory and Applications all top 5 Cited in 7 Fields 9 Statistics (62-XX) 5 Probability theory and stochastic processes (60-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 2 Numerical analysis (65-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year