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 highdimensional 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 highdimensional 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 highdimensional data analysis. 
Homepage:  http://www.worldscientific.com/doi/10.1142/S2010326315500197 
Keywords:  limiting spectral distribution; sample covariance matrix; Stieltjes transform; highdimensional 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 1330.65029 Dobriban, Edgar 
2014

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Cited by 20 Authors
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Cited in 9 Serials
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