Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality

• Published in: Journal of the Royal Statistical Society Series C: Applied Statistics Vol. 71; no. 1; pp. 119 - 147
• Main Authors: Perrot‐Dockès, M., Lévy‐Leduc, C., Rajjou, L.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2022; Wiley
• Subjects: block matrix; covariance estimation; Covariance matrix; Estimation; Genomics; high dimension; Matrices; Methodology; Permutations; reduction of dimension; Sparse matrices; Statistical methods; Statistics; SVD; SVD; covariance estimation; reduction of dimension; block matrix; high dimension
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/rssc.12524

Motivated by an application in high‐throughput genomics and metabolomics, we propose a novel and fully data‐driven approach for estimating large block structured sparse covariance matrices in the case where the number of variables is much larger than the number of samples without limiting ourselves to block diagonal matrices. Our approach consists in approximating such a covariance matrix by the sum of a low‐rank sparse matrix and a diagonal matrix. Our methodology also can deal with matrices for which the block structure appears only if the columns and rows are permuted according to an unknown permutation. Our technique is implemented in the R package BlockCov which is available from the Comprehensive R Archive Network (CRAN) and from GitHub. In order to illustrate the statistical and numerical performance of our package some numerical experiments are provided as well as a thorough comparison with alternative methods. Finally, our approach is applied to the use of ‘multi‐omic’ approaches for studying seed quality.